v=14 


 System No. 1 
 |Aut(S)|=20160 


 Subsystem No. 0 
 |Aut(T)|=1344 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,0},{2,12,13},{3,7,11},{3,8,12},{3,9,13},{3,10,0},
 {4,7,12},{4,8,11},{4,9,0},{4,10,13},{5,7,13},{5,8,0},{5,9,11},{5,10,12},
 {6,7,0},{6,8,13},{6,9,12},{6,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 2)(3 5 4 6)(7 9 8 12 11 10 13)
      B_1={{2,3,6},{2,4,5},{2,7,10},{2,8,9},{2,11,0},{2,12,13},
      {5,7,13},{5,8,0},{5,9,11},{5,10,12},{6,7,0},{6,8,13},
      {6,9,12},{6,10,11}}
   B: \alpha=(0)(1 2)(3 5 4 6)(7 9 8 10)(11 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,11},{3,8,12},{3,9,13},{3,10,0},{4,7,12},{4,8,11},
      {4,9,0},{4,10,13}}
   C: \alpha=(0 1 3 6 10 4)(2 11 13 9 12 5)(7 8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,11,13},{2,4,5},{2,7,10},
      {2,12,13},{3,7,11},{4,7,12},{4,9,0},{5,7,13},{6,7,0},
      {6,9,12},{6,10,11}}
   E: \alpha=(0)(1 2)(3 5 4 6)(7 10 8 9)(11 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,11},{3,8,12},{3,9,13},{3,10,0},{4,7,12},{4,8,11},
      {4,9,0},{4,10,13}}
 # of antimorphisms of SASC-graph: 16128 (fair: 1680) 
 # of halving permutations: 588 (fair: 252; strong: 252) 


 System No. 2 
 |Aut(S)|=192 


 Subsystem No. 0 
 |Aut(T)|=192 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,0},{2,12,13},{3,7,11},{3,8,12},{3,9,13},{3,10,0},
 {4,7,12},{4,8,11},{4,9,0},{4,10,13},{5,7,0},{5,8,13},{5,9,12},{5,10,11},
 {6,7,13},{6,8,0},{6,9,11},{6,10,12}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 2)(3 5 4 6)(7 9 8 12 11 10 13)
      B_1={{2,3,6},{2,4,5},{2,7,10},{2,8,9},{2,11,0},{2,12,13},
      {5,7,0},{5,8,13},{5,9,12},{5,10,11},{6,7,13},{6,8,0},
      {6,9,11},{6,10,12}}
   B: \alpha=(0)(1 2)(3 5 4 6)(7 10 8 9)(11 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,11},{3,8,12},{3,9,13},{3,10,0},{4,7,12},{4,8,11},
      {4,9,0},{4,10,13}}
   D: \alpha=(0 1 3 8 13 2 4 7)(5 12 6 11)(9 10)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{2,3,6},{2,4,5},
      {2,7,10},{2,8,9},{5,7,0},{5,8,13},{5,9,12},{6,7,13},
      {6,8,0},{6,9,11}}
   E: \alpha=(0)(1 2)(3 5 4 6)(7 9 8 10)(11 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,11},{3,8,12},{3,9,13},{3,10,0},{4,7,12},{4,8,11},
      {4,9,0},{4,10,13}}
 # of antimorphisms of SASC-graph: 7344 (fair: 1680) 
 # of halving permutations: 204 (fair: 204; strong: 60) 


 Subsystem No. 1 
 |Aut(T)|=32 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,1},{2,12,13},{3,7,11},{3,8,12},{3,9,13},{3,10,1},
 {4,7,12},{4,8,11},{4,9,1},{4,10,13},{5,7,1},{5,8,13},{5,9,12},{5,10,11},
 {6,7,13},{6,8,1},{6,9,11},{6,10,12}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 11 5 13 4 12 6)(2)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,5},{2,7,10},
      {3,7,11},{3,8,12},{4,7,12},{4,8,11},{5,7,1},{5,8,13},
      {6,7,13},{6,8,1}}
   B: \alpha=(0)(1 3 12 5)(2)(4 11 6 13)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,5},{2,7,10},
      {3,7,11},{3,8,12},{4,7,12},{4,8,11},{5,7,1},{5,8,13},
      {6,7,13},{6,8,1}}
   C: \alpha=(0 3 2 5)(1)(4 6)(7 9 8 13 10 12 11)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,4,5},
      {2,7,10},{2,8,9},{2,11,1},{2,12,13},{4,7,12},{4,8,11},
      {4,9,1},{4,10,13}}
   D: \alpha=(0)(1 3 11 6)(2)(4 12 5 13)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,5},{2,7,10},
      {3,7,11},{3,8,12},{4,7,12},{4,8,11},{5,7,1},{5,8,13},
      {6,7,13},{6,8,1}}
   E: \alpha=(0)(1 7 11 10)(2)(3 5)(4 6)(8 12 9 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,6},{2,7,10},{2,8,9},
      {3,7,11},{3,8,12},{3,9,13},{3,10,1},{4,7,12},{4,8,11},
      {4,9,1},{4,10,13}}
 # of antimorphisms of SASC-graph: 1781 (fair: 265) 
 # of halving permutations: 140 (fair: 12; strong: 4) 


 Subsystem No. 7 
 |Aut(T)|=24 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,9},{2,11,7},{2,12,13},
 {3,8,12},{3,9,13},{3,10,7},{4,8,11},{4,9,7},{4,10,13},{5,8,13},{5,9,12},
 {5,10,11},{6,8,7},{6,9,11},{6,10,12}}
 I={{0,8},{1,9},{2,10},{3,11},{4,12},{5,7},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 9 11 2 4 10 12)(5 7)(6 13)(8)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,4,6},{1,8,10},
      {2,3,6},{2,4,5},{2,8,9},{5,8,13},{5,9,12},{5,10,11},
      {6,9,11},{6,10,12}}
   B: \alpha=(0)(1 3 2 4)(5 7)(6 13)(8)(9 11 10 12)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,8,10},{1,11,13},
      {2,4,5},{2,8,9},{2,12,13},{3,9,13},{4,10,13},{5,8,13},
      {5,9,12},{5,10,11}}
   C: \alpha=(0)(1 3 10 11 2 4 9 12)(5 7)(6 13)(8)
      B_1={{0,3,4},{0,11,12},{0,13,7},{1,11,13},{1,12,7},{2,11,7},
      {2,12,13},{3,8,12},{3,9,13},{3,10,7},{4,8,11},{4,9,7},
      {4,10,13},{6,8,7}}
 # of antimorphisms of SASC-graph: 3366 (fair: 366) 
 # of halving permutations: 216 (fair: 0; strong: 0) 


 System No. 3 
 |Aut(S)|=96 


 Subsystem No. 0 
 |Aut(T)|=32 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,0},{2,12,13},{3,7,11},{3,8,12},{3,9,13},{3,10,0},
 {4,7,13},{4,8,0},{4,9,11},{4,10,12},{5,7,0},{5,8,13},{5,9,12},{5,10,11},
 {6,7,12},{6,8,11},{6,9,0},{6,10,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 2 4)(5 6)(7 8 11 10 12 13 9)
      B_1={{1,4,6},{2,3,6},{3,7,11},{3,8,12},{3,9,13},{3,10,0},
      {4,7,13},{4,8,0},{4,9,11},{4,10,12},{6,7,12},{6,8,11},
      {6,9,0},{6,10,13}}
   B: \alpha=(0)(1 3 2 4)(5 6)(7 8)(9 11 10 12)(13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,4,5},
      {2,7,10},{2,8,9},{2,11,0},{2,12,13},{5,7,0},{5,8,13},
      {5,9,12},{5,10,11}}
   C: \alpha=(0)(1 3 2 4)(5 6)(7 8 12 13 10 11 9)
      B_1={{1,4,6},{2,3,6},{3,7,11},{3,8,12},{3,9,13},{3,10,0},
      {4,7,13},{4,8,0},{4,9,11},{4,10,12},{6,7,12},{6,8,11},
      {6,9,0},{6,10,13}}
   E: \alpha=(0 7 12 9)(1)(2)(3 4)(5 6)(8 11 10 13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{2,3,6},{2,7,10},{2,8,9},
      {3,7,11},{3,8,12},{3,9,13},{3,10,0},{5,7,0},{5,8,13},
      {5,9,12},{5,10,11}}
 # of antimorphisms of SASC-graph: 821 (fair: 201) 
 # of halving permutations: 132 (fair: 4; strong: 4) 


 Subsystem No. 3 
 |Aut(T)|=24 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,9},{2,11,3},{2,12,13},
 {4,7,13},{4,8,3},{4,9,11},{4,10,12},{5,7,3},{5,8,13},{5,9,12},{5,10,11},
 {6,7,12},{6,8,11},{6,9,3},{6,10,13}}
 I={{0,4},{1,5},{2,6},{7,11},{8,12},{9,13},{10,3}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5)(2 4 6)(3 7 9 12)(8 10 11 13)
      B_1={{0,5,6},{0,9,10},{0,13,3},{2,4,5},{2,8,9},{2,11,3},
      {4,8,3},{4,9,11},{5,7,3},{5,8,13},{5,9,12},{5,10,11},
      {6,8,11},{6,9,3}}
   B: \alpha=(0)(1 5)(2 6)(3 7 9 12)(4)(8 10 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{2,7,10},{2,12,13},{4,7,13},{4,10,12},
      {6,7,12},{6,10,13}}
   C: \alpha=(0 1 4 5)(2 6)(3)(7 9 11 10 13 12 8)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{2,4,5},
      {4,7,13},{4,8,3},{4,9,11},{4,10,12},{6,7,12},{6,8,11},
      {6,9,3},{6,10,13}}
   D: \alpha=(0 4)(1 2 5 6)(3)(7 11)(8 9 12 13)(10)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},
      {2,7,10},{2,8,9},{2,11,3},{2,12,13},{6,7,12},{6,8,11},
      {6,9,3},{6,10,13}}
 # of antimorphisms of SASC-graph: 531 (fair: 105) 
 # of halving permutations: 72 (fair: 24; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=12 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,9},{2,11,7},{2,12,13},
 {3,8,12},{3,9,13},{3,10,7},{4,8,7},{4,9,11},{4,10,12},{5,8,13},{5,9,12},
 {5,10,11},{6,8,11},{6,9,7},{6,10,13}}
 I={{0,8},{1,9},{2,10},{3,11},{4,13},{5,7},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 9 11 2 6 10 12)(4 13)(5 7)(8)
      B_1={{0,1,2},{0,9,10},{0,13,7},{1,8,10},{1,11,13},{1,12,7},
      {2,8,9},{2,11,7},{2,12,13},{3,9,13},{3,10,7},{4,8,7},
      {6,9,7},{6,10,13}}
   B: \alpha=(0)(1 3 9 11)(2 6 10 12)(4 13)(5 7)(8)
      B_1={{0,1,2},{0,9,10},{0,13,7},{1,8,10},{1,11,13},{1,12,7},
      {2,8,9},{2,11,7},{2,12,13},{3,9,13},{3,10,7},{4,8,7},
      {6,9,7},{6,10,13}}
 # of antimorphisms of SASC-graph: 864 (fair: 96) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 4 
 |Aut(S)|=8 


 Subsystem No. 0 
 |Aut(T)|=8 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,0},{2,12,13},{3,7,11},{3,8,12},{3,9,13},{3,10,0},
 {4,7,13},{4,8,11},{4,9,0},{4,10,12},{5,7,0},{5,8,13},{5,9,12},{5,10,11},
 {6,7,12},{6,8,0},{6,9,11},{6,10,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 2 4)(5 6)(7 8 11 10 12 13 9)
      B_1={{1,4,6},{2,3,6},{3,7,11},{3,8,12},{3,9,13},{3,10,0},
      {4,7,13},{4,8,11},{4,9,0},{4,10,12},{6,7,12},{6,8,0},
      {6,9,11},{6,10,13}}
   B: \alpha=(0)(1 3 2 4)(5 6)(7 8)(9 11 10 12)(13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,4,5},
      {2,7,10},{2,8,9},{2,11,0},{2,12,13},{5,7,0},{5,8,13},
      {5,9,12},{5,10,11}}
   C: \alpha=(0 3 12 4 11 5 13 6)(1 2)(7 10 8 9)
      B_1={{2,3,6},{2,4,5},{2,7,10},{2,8,9},{2,11,0},{2,12,13},
      {3,9,13},{3,10,0},{4,9,0},{4,10,12},{5,9,12},{5,10,11},
      {6,9,11},{6,10,13}}
   D: \alpha=(0 3 11 5)(1 2)(4 12 6 13)(7 10 8 9)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,11},{3,8,12},{4,7,13},{4,8,11},{5,7,0},{5,8,13},
      {6,7,12},{6,8,0}}
 # of antimorphisms of SASC-graph: 1246 (fair: 342) 
 # of halving permutations: 20 (fair: 4; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=8 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,1},{2,12,13},{3,7,11},{3,8,12},{3,9,13},{3,10,1},
 {4,7,13},{4,8,11},{4,9,1},{4,10,12},{5,7,1},{5,8,13},{5,9,12},{5,10,11},
 {6,7,12},{6,8,1},{6,9,11},{6,10,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 7 11 10)(2 4 6)(3 5)(8 12 9 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,6},{2,7,10},{2,12,13},
      {3,7,11},{3,8,12},{3,9,13},{3,10,1},{4,7,13},{4,10,12},
      {6,7,12},{6,10,13}}
   B: \alpha=(0)(1 7 11 10)(2)(3 5)(4 6)(8 12 9 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,6},{2,7,10},{2,8,9},
      {3,7,11},{3,8,12},{3,9,13},{3,10,1},{4,7,13},{4,10,12},
      {6,7,12},{6,10,13}}
   E: \alpha=(0)(1 8 11 9)(2)(3 5)(4 6)(7 12 10 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,6},{2,7,10},{2,8,9},
      {3,7,11},{3,8,12},{3,9,13},{3,10,1},{4,7,13},{4,8,11},
      {4,9,1},{4,10,12}}
 # of antimorphisms of SASC-graph: 405 (fair: 89) 
 # of halving permutations: 2 (fair: 2; strong: 2) 


 Subsystem No. 2 
 |Aut(T)|=8 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,11},{3,8,12},{3,9,13},{3,10,2},
 {4,7,13},{4,8,11},{4,9,2},{4,10,12},{5,7,2},{5,8,13},{5,9,12},{5,10,11},
 {6,7,12},{6,8,2},{6,9,11},{6,10,13}}
 I={{0,1},{3,6},{4,5},{7,10},{8,9},{11,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 7 8 10 9 12 11 13)(3 4 6 5)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,2},
      {4,7,13},{4,8,11},{4,9,2},{4,10,12},{5,7,2},{5,8,13},
      {5,9,12},{5,10,11}}
   B: \alpha=(0)(1)(2 7 11 10)(3 6)(4 5)(8 13 9 12)
      B_1={{0,3,4},{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,8,10},
      {3,7,11},{3,8,12},{3,9,13},{3,10,2},{4,7,13},{4,8,11},
      {4,9,2},{4,10,12}}
   D: \alpha=(0)(1)(2 7 13 9 11 10 12 8)(3 6)(4 5)
      B_1={{0,3,4},{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,8,10},
      {3,7,11},{3,8,12},{3,9,13},{3,10,2},{5,7,2},{5,8,13},
      {5,9,12},{5,10,11}}
 # of antimorphisms of SASC-graph: 776 (fair: 200) 
 # of halving permutations: 10 (fair: 10; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,9},{2,11,3},{2,12,13},
 {4,7,13},{4,8,11},{4,9,3},{4,10,12},{5,7,3},{5,8,13},{5,9,12},{5,10,11},
 {6,7,12},{6,8,3},{6,9,11},{6,10,13}}
 I={{0,4},{1,5},{2,6},{7,11},{8,12},{9,13},{10,3}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5)(2 4 6)(3 10)(7 11)(8 12)(9 13)
      B_1={{0,5,6},{0,11,12},{0,13,3},{1,8,10},{1,11,13},{2,4,5},
      {2,8,9},{2,11,3},{4,8,11},{4,9,3},{5,8,13},{5,10,11},
      {6,8,3},{6,9,11}}
   B: \alpha=(0)(1 5)(2 6)(3 7 9 12)(4)(8 10 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{2,7,10},{2,8,9},{2,11,3},{2,12,13},
      {4,8,11},{4,9,3}}
   C: \alpha=(0)(1 5)(2 4 6)(3 7 9 12)(8 10 11 13)
      B_1={{0,5,6},{0,9,10},{0,13,3},{2,4,5},{2,8,9},{2,11,3},
      {4,8,11},{4,9,3},{5,7,3},{5,8,13},{5,9,12},{5,10,11},
      {6,8,3},{6,9,11}}
 # of antimorphisms of SASC-graph: 345 (fair: 43) 
 # of halving permutations: 20 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,10},{2,8,9},{2,11,4},{2,12,13},
 {3,7,11},{3,8,12},{3,9,13},{3,10,4},{5,7,4},{5,8,13},{5,9,12},{5,10,11},
 {6,7,12},{6,8,4},{6,9,11},{6,10,13}}
 I={{0,3},{1,6},{2,5},{7,13},{8,11},{9,4},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 4 8)(2 12 6 9)(3 5 7 11 10 13)
      B_1={{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,8,10},{1,12,4},
      {2,3,6},{2,7,10},{2,8,9},{3,7,11},{3,8,12},{3,10,4},
      {6,7,12},{6,10,13}}
   B: \alpha=(0 1 7 11)(2 10 5 12)(3 6 13 8)(4 9)
      B_1={{0,1,2},{0,13,4},{1,3,5},{1,11,13},{1,12,4},{2,3,6},
      {2,11,4},{2,12,13},{3,7,11},{3,9,13},{3,10,4},{5,7,4},
      {5,8,13},{5,10,11}}
   C: \alpha=(0 2 4 8 1 11 6 7)(3 5 10 13 9 12)
      B_1={{0,7,8},{0,9,10},{1,7,9},{1,8,10},{2,3,6},{2,7,10},
      {2,8,9},{2,11,4},{3,7,11},{3,8,12},{3,9,13},{3,10,4},
      {5,10,11},{6,9,11}}
 # of antimorphisms of SASC-graph: 240 (fair: 8) 
 # of halving permutations: 24 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,9},{2,11,7},{2,12,13},
 {3,8,12},{3,9,13},{3,10,7},{4,8,11},{4,9,7},{4,10,12},{5,8,13},{5,9,12},
 {5,10,11},{6,8,7},{6,9,11},{6,10,13}}
 I={{0,8},{1,9},{2,10},{3,11},{4,13},{5,7},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 7 2 5 10 13)(4 11 6 8 9 12)
      B_1={{0,11,12},{0,13,7},{1,3,5},{1,8,10},{1,11,13},{1,12,7},
      {2,11,7},{2,12,13},{3,8,12},{4,8,11},{5,8,13},{5,9,12},
      {5,10,11},{6,8,7}}
   B: \alpha=(0 2 4 11)(1 6 9 12)(3 8 10 13)(5 7)
      B_1={{0,1,2},{0,13,7},{1,8,10},{1,11,13},{1,12,7},{2,8,9},
      {2,11,7},{2,12,13},{3,9,13},{3,10,7},{4,8,11},{4,9,7},
      {6,8,7},{6,9,11}}
   C: \alpha=(0 2 12 9 4 1 13 3)(5 7)(6 11 8 10)
      B_1={{0,1,2},{0,5,6},{1,3,5},{1,4,6},{1,8,10},{2,3,6},
      {2,4,5},{2,8,9},{3,8,12},{3,9,13},{5,8,13},{5,9,12},
      {5,10,11},{6,9,11}}
 # of antimorphisms of SASC-graph: 345 (fair: 37) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,11,8},{2,12,13},
 {3,7,11},{3,9,13},{3,10,8},{4,7,13},{4,9,8},{4,10,12},{5,7,8},{5,9,12},
 {5,10,11},{6,7,12},{6,9,11},{6,10,13}}
 I={{0,7},{1,10},{2,9},{3,12},{4,11},{5,13},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 9 12 2 4 10 11)(5 13)(6 8)(7)
      B_1={{0,3,4},{0,11,12},{0,13,8},{1,4,6},{1,11,13},{2,3,6},
      {2,12,13},{3,7,11},{3,9,13},{4,7,13},{4,10,12},{6,7,12},
      {6,9,11},{6,10,13}}
   B: \alpha=(0)(1 3 2 4)(5 13)(6 8)(7)(9 11 10 12)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,7,9},{1,12,8},
      {2,4,5},{2,7,10},{2,11,8},{3,10,8},{4,9,8},{5,7,8},
      {5,9,12},{5,10,11}}
   C: \alpha=(0 1 3 13 2 5 9 8)(4 7 10 11 6 12)
      B_1={{0,11,12},{0,13,8},{1,3,5},{1,7,9},{1,11,13},{1,12,8},
      {2,11,8},{2,12,13},{3,7,11},{4,7,13},{5,7,8},{5,9,12},
      {5,10,11},{6,7,12}}
   D: \alpha=(0 9 7 2)(1 10)(3 8 12 6)(4)(5 13)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,8},{1,7,9},
      {1,11,13},{3,7,11},{3,10,8},{4,7,13},{4,10,12},{5,7,8},
      {6,7,12},{6,10,13}}
 # of antimorphisms of SASC-graph: 852 (fair: 144) 
 # of halving permutations: 34 (fair: 6; strong: 0) 


 System No. 5 
 |Aut(S)|=32 


 Subsystem No. 0 
 |Aut(T)|=16 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,0},{2,12,13},{3,7,11},{3,8,12},{3,9,0},{3,10,13},
 {4,7,13},{4,8,0},{4,9,12},{4,10,11},{5,7,12},{5,8,11},{5,9,13},{5,10,0},
 {6,7,0},{6,8,13},{6,9,11},{6,10,12}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 2 4)(5 6)(7 8 11 9 12 13 10)
      B_1={{1,4,6},{2,3,6},{3,7,11},{3,8,12},{3,9,0},{3,10,13},
      {4,7,13},{4,8,0},{4,9,12},{4,10,11},{5,7,12},{5,8,11},
      {5,9,13},{5,10,0}}
   B: \alpha=(0)(1 3 2 4)(5 6)(7 8)(9 11 10 12)(13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,4,5},
      {2,7,10},{2,8,9},{2,11,0},{2,12,13},{6,7,0},{6,8,13},
      {6,9,11},{6,10,12}}
   D: \alpha=(0 3 13 4)(1)(2)(5 11 6 12)(7 8)(9 10)
      B_1={{1,3,5},{1,4,6},{1,7,9},{2,3,6},{2,4,5},{2,7,10},
      {3,7,11},{3,9,0},{4,7,13},{4,9,12},{5,7,12},{5,9,13},
      {6,7,0},{6,9,11}}
 # of antimorphisms of SASC-graph: 793 (fair: 201) 
 # of halving permutations: 16 (fair: 16; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=32 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,1},{2,12,13},{3,7,11},{3,8,12},{3,9,1},{3,10,13},
 {4,7,13},{4,8,1},{4,9,12},{4,10,11},{5,7,12},{5,8,11},{5,9,13},{5,10,1},
 {6,7,1},{6,8,13},{6,9,11},{6,10,12}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 11 6)(2 8 10)(4 12 5 13)(7 9)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,7,10},{2,12,13},
      {3,7,11},{3,8,12},{3,10,13},{4,7,13},{5,7,12},{6,7,1},
      {6,8,13},{6,10,12}}
   B: \alpha=(0)(1 3 11 6)(2)(4 12 5 13)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,5},{2,7,10},
      {3,7,11},{3,8,12},{3,10,13},{4,7,13},{5,7,12},{6,7,1},
      {6,8,13},{6,10,12}}
   E: \alpha=(0)(1 12)(2)(3 5)(4 6)(7 9)(8 10)(11 13)
      B_1={{0,3,4},{0,7,8},{0,11,12},{2,3,6},{2,7,10},{2,11,1},
      {3,7,11},{3,8,12},{3,9,1},{3,10,13},{4,7,13},{4,8,1},
      {4,9,12},{4,10,11}}
 # of antimorphisms of SASC-graph: 369 (fair: 121) 
 # of halving permutations: 13 (fair: 13; strong: 13) 


 Subsystem No. 3 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,9},{2,11,3},{2,12,13},
 {4,7,13},{4,8,3},{4,9,12},{4,10,11},{5,7,12},{5,8,11},{5,9,13},{5,10,3},
 {6,7,3},{6,8,13},{6,9,11},{6,10,12}}
 I={{0,4},{1,5},{2,6},{7,11},{8,12},{9,3},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 10 2 12 5 9)(4 6 7 13 8 11)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,13,3},{1,4,6},{1,12,3},
      {2,4,5},{2,7,10},{2,8,9},{2,11,3},{4,7,13},{4,8,3},
      {5,7,12},{5,8,11}}
   B: \alpha=(0)(1 5)(2 6)(3 7 12 10)(4)(8 13 9 11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{4,7,13},{4,10,11},{6,7,3},{6,8,13},
      {6,9,11},{6,10,12}}
   C: \alpha=(0 2 3 7 13 9 1 11 6 4 5 10)(8 12)
      B_1={{0,7,8},{0,9,10},{1,7,9},{1,8,10},{2,4,5},{2,7,10},
      {2,8,9},{2,11,3},{4,7,13},{4,8,3},{4,10,11},{5,8,11},
      {6,8,13},{6,9,11}}
 # of antimorphisms of SASC-graph: 588 (fair: 76) 
 # of halving permutations: 24 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=8 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,5},{2,7,10},{2,8,9},{2,12,13},
 {3,8,12},{3,9,11},{3,10,13},{4,7,13},{4,8,11},{4,9,12},{5,7,12},{5,9,13},
 {5,10,11},{6,7,11},{6,8,13},{6,10,12}}
 I={{0,12},{1,13},{2,11},{3,7},{4,10},{5,8},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 11 7 2 5 13 8)(4 10)(6 9)(12)
      B_1={{0,3,4},{0,5,6},{0,7,8},{1,3,5},{1,4,6},{2,3,6},
      {2,4,5},{3,8,12},{4,7,13},{4,8,11},{5,7,12},{6,7,11},
      {6,8,13},{6,10,12}}
   B: \alpha=(0)(1 3 11 8)(2 5 13 7)(4 10)(6 9)(12)
      B_1={{0,1,2},{0,9,10},{0,13,11},{1,7,9},{1,8,10},{1,12,11},
      {2,7,10},{2,8,9},{2,12,13},{3,9,11},{3,10,13},{4,9,12},
      {5,9,13},{5,10,11}}
   C: \alpha=(0 1 3 8)(2 6 13 7)(4 10)(5 12 11 9)
      B_1={{0,7,8},{0,13,11},{1,3,5},{1,4,6},{1,8,10},{1,12,11},
      {2,3,6},{2,4,5},{2,8,9},{2,12,13},{4,7,13},{4,8,11},
      {5,9,13},{5,10,11}}
   D: \alpha=(0 7 4 2)(1 8 13 5)(3 10 11 12)(6 9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,13,11},{1,3,5},
      {1,4,6},{1,12,11},{3,9,11},{3,10,13},{4,7,13},{4,8,11},
      {4,9,12},{6,8,13}}
 # of antimorphisms of SASC-graph: 754 (fair: 90) 
 # of halving permutations: 52 (fair: 4; strong: 0) 


 System No. 6 
 |Aut(S)|=24 


 Subsystem No. 0 
 |Aut(T)|=8 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,0},{2,12,13},{3,7,11},{3,8,12},{3,9,0},{3,10,13},
 {4,7,13},{4,8,0},{4,9,12},{4,10,11},{5,7,12},{5,8,13},{5,9,11},{5,10,0},
 {6,7,0},{6,8,11},{6,9,13},{6,10,12}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5 2 6)(3 4)(7 8 9 11 10 13 12)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},
      {2,7,10},{2,8,9},{2,11,0},{2,12,13},{4,7,13},{4,8,0},
      {4,9,12},{4,10,11}}
   B: \alpha=(0)(1 5 2 6)(3 4)(7 8)(9 11 10 12)(13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},
      {2,7,10},{2,8,9},{2,11,0},{2,12,13},{4,7,13},{4,8,0},
      {4,9,12},{4,10,11}}
   C: \alpha=(0)(1 5 2 6)(3 4)(7 8 9 13 12 10 11)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},
      {2,7,10},{2,8,9},{2,11,0},{2,12,13},{4,7,13},{4,8,0},
      {4,9,12},{4,10,11}}
   E: \alpha=(0 8 12 9)(1 2)(3 4)(5)(6)(7 11 10 13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,11},{3,8,12},{3,9,0},{3,10,13},{5,7,12},{5,10,0},
      {6,7,0},{6,10,12}}
 # of antimorphisms of SASC-graph: 385 (fair: 89) 
 # of halving permutations: 82 (fair: 2; strong: 2) 


 Subsystem No. 3 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,9},{2,11,3},{2,12,13},
 {4,7,13},{4,8,3},{4,9,12},{4,10,11},{5,7,12},{5,8,13},{5,9,11},{5,10,3},
 {6,7,3},{6,8,11},{6,9,13},{6,10,12}}
 I={{0,4},{1,5},{2,6},{7,11},{8,12},{9,3},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5)(2 6)(3 4 9)(7 11)(8 12)(10 13)
      B_1={{0,1,2},{0,7,8},{0,9,10},{2,4,5},{2,7,10},{2,8,9},
      {2,11,3},{2,12,13},{4,8,3},{4,10,11},{5,7,12},{5,8,13},
      {5,9,11},{5,10,3}}
   B: \alpha=(0)(1 5)(2 6)(3 7 12 10)(4)(8 13 9 11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{4,7,13},{4,10,11},{6,7,3},{6,8,11},
      {6,9,13},{6,10,12}}
   C: \alpha=(0 1 7 12)(2 9 5 4 6 3 8 11)(10 13)
      B_1={{0,11,12},{0,13,3},{1,4,6},{1,7,9},{1,11,13},{1,12,3},
      {2,11,3},{2,12,13},{4,7,13},{4,8,3},{4,9,12},{5,8,13},
      {5,9,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 197 (fair: 13) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=4 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,7,10},{2,8,9},{2,11,5},{2,12,13},
 {3,7,11},{3,8,12},{3,9,5},{3,10,13},{4,7,13},{4,8,5},{4,9,12},{4,10,11},
 {6,7,5},{6,8,11},{6,9,13},{6,10,12}}
 I={{0,6},{1,3},{2,4},{7,12},{8,13},{9,11},{10,5}}
 Examples of antimorphisms:
   A: \alpha=(0 1 4 5)(2 10 8 12)(3 13 7 6)(9 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{1,7,9},{2,3,6},
      {2,7,10},{2,8,9},{3,7,11},{3,8,12},{3,9,5},{4,7,13},
      {4,8,5},{4,9,12}}
   B: \alpha=(0)(1 3)(2 4)(5 8 12 9)(6)(7 11 10 13)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,5},{4,7,13},{4,8,5},{4,9,12},{4,10,11},
      {6,7,5},{6,10,12}}
   C: \alpha=(0 1 11 8)(2 13 6 7)(3 10 12 9 5 4)
      B_1={{0,7,8},{0,9,10},{1,4,6},{1,7,9},{1,8,10},{1,11,13},
      {2,7,10},{2,8,9},{3,10,13},{4,7,13},{4,8,5},{4,9,12},
      {4,10,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 251 (fair: 27) 
 # of halving permutations: 16 (fair: 0; strong: 0) 


 System No. 7 
 |Aut(S)|=288 


 Subsystem No. 0 
 |Aut(T)|=96 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,9},{2,11,0},{2,12,13},{3,7,11},{3,8,13},{3,9,0},{3,10,12},
 {4,7,0},{4,8,12},{4,9,11},{4,10,13},{5,7,12},{5,8,0},{5,9,13},{5,10,11},
 {6,7,13},{6,8,11},{6,9,12},{6,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 3 5 7)(1 2)(4 6 10 12)(8 13 9 11)
      B_1={{2,3,6},{2,4,5},{2,7,10},{2,8,9},{2,11,0},{2,12,13},
      {3,9,0},{4,8,12},{5,7,12},{5,8,0},{5,9,13},{6,8,11},
      {6,9,12},{6,10,0}}
   B: \alpha=(0)(1 2)(3 4)(5 7 9 11)(6 8 10 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,11},{3,9,0},{4,8,12},{4,10,13},{5,8,0},{5,10,11},
      {6,7,13},{6,9,12}}
   C: \alpha=(0 3 7 12 4 10)(1 2)(5 8 13 6 9 11)
      B_1={{2,3,6},{2,4,5},{2,7,10},{2,8,9},{2,11,0},{2,12,13},
      {3,9,0},{4,7,0},{4,9,11},{4,10,13},{5,7,12},{5,8,0},
      {6,7,13},{6,8,11}}
   E: \alpha=(0)(1 2)(3 7 5 10)(4 8 6 9)(11 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,11},{3,8,13},{3,9,0},{4,8,12},{5,8,0},{5,9,13},
      {5,10,11},{6,9,12}}
 # of antimorphisms of SASC-graph: 585 (fair: 273) 
 # of halving permutations: 69 (fair: 45; strong: 45) 


 Subsystem No. 3 
 |Aut(T)|=24 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,9},{2,11,3},{2,12,13},
 {4,7,3},{4,8,12},{4,9,11},{4,10,13},{5,7,12},{5,8,3},{5,9,13},{5,10,11},
 {6,7,13},{6,8,11},{6,9,12},{6,10,3}}
 I={{0,4},{1,5},{2,6},{7,11},{8,13},{9,3},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 3 5 13)(2 4 7 8 9 11)(10 12)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,7,9},{1,8,10},{2,7,10},
      {2,8,9},{2,11,3},{4,7,3},{4,10,13},{5,9,13},{5,10,11},
      {6,7,13},{6,10,3}}
   B: \alpha=(0)(1 5)(2 6)(3 8 11 10)(4)(7 12 9 13)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{4,7,3},{4,9,11},{6,7,13},{6,8,11},
      {6,9,12},{6,10,3}}
 # of antimorphisms of SASC-graph: 54 (fair: 6) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 8 
 |Aut(S)|=4 


 Subsystem No. 0 
 |Aut(T)|=4 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,9},{3,10,13},{3,11,0},
 {4,7,0},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,0},{5,9,11},{5,10,12},
 {6,7,11},{6,8,12},{6,9,13},{6,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5 2 6)(3 4)(7 9 10 11 8 12 13)
      B_1={{1,4,6},{2,4,5},{4,7,0},{4,8,13},{4,9,12},{4,10,11},
      {5,7,13},{5,8,0},{5,9,11},{5,10,12},{6,7,11},{6,8,12},
      {6,9,13},{6,10,0}}
   B: \alpha=(0)(1 5 2 6)(3 4)(7 11 8 12)(9 10)(13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},
      {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,9},
      {3,10,13},{3,11,0}}
 # of antimorphisms of SASC-graph: 212 (fair: 52) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=4 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,9},{3,10,13},{3,11,1},
 {4,7,1},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,1},{5,9,11},{5,10,12},
 {6,7,11},{6,8,12},{6,9,13},{6,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 12)(2 3 5)(4 6)(7 9)(8 10)(11 13)
      B_1={{0,3,4},{0,7,8},{0,11,12},{2,4,5},{2,7,10},{2,12,13},
      {3,7,12},{3,10,13},{4,7,1},{4,10,11},{5,7,13},{5,10,12},
      {6,7,11},{6,10,1}}
   B: \alpha=(0)(1 7 11 10)(2)(3 5)(4 6)(8 12 9 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,6},{2,7,10},{2,12,13},
      {3,7,12},{3,10,13},{4,7,1},{4,8,13},{4,9,12},{4,10,11},
      {5,7,13},{5,10,12}}
   C: \alpha=(0)(1 7 11 10)(2 3 5)(4 6)(8 12 9 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,4,5},{2,7,10},{2,12,13},
      {3,7,12},{3,10,13},{4,7,1},{4,8,13},{4,9,12},{4,10,11},
      {5,7,13},{5,10,12}}
 # of antimorphisms of SASC-graph: 177 (fair: 35) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=4 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,9},{3,10,13},{3,11,2},
 {4,7,2},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,2},{5,9,11},{5,10,12},
 {6,7,11},{6,8,12},{6,9,13},{6,10,2}}
 I={{0,1},{3,6},{4,5},{7,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 3 2 7)(1 5 11 10)(4 8 6 9)(12 13)
      B_1={{0,3,4},{0,5,6},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
      {1,11,13},{1,12,2},{4,7,2},{4,8,13},{4,10,11},{6,7,11},
      {6,9,13},{6,10,2}}
   C: \alpha=(0 5 2 10 1 3 11 7)(4 9 6 8)(12 13)
      B_1={{0,3,4},{0,5,6},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
      {1,11,13},{1,12,2},{4,7,2},{4,8,13},{4,10,11},{6,7,11},
      {6,9,13},{6,10,2}}
 # of antimorphisms of SASC-graph: 64 (fair: 0) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,11},{2,9,3},{2,12,13},
 {4,7,3},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,3},{5,9,11},{5,10,12},
 {6,7,11},{6,8,12},{6,9,13},{6,10,3}}
 I={{0,4},{1,5},{2,6},{7,12},{8,9},{10,13},{11,3}}
 Examples of antimorphisms:
   A: \alpha=(0 4)(1 5 6)(2)(3 7 8 13)(9 10 11 12)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},
      {1,7,9},{1,11,13},{2,7,10},{2,12,13},{5,7,13},{5,9,11},
      {6,7,11},{6,9,13}}
   B: \alpha=(0 4)(1 5)(2)(3 7 8 13)(6)(9 10 11 12)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},
      {1,7,9},{1,11,13},{2,7,10},{2,12,13},{5,7,13},{5,9,11},
      {6,7,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 25 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,10},{2,8,11},{2,9,4},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,4},{5,7,13},{5,8,4},{5,9,11},{5,10,12},
 {6,7,11},{6,8,12},{6,9,13},{6,10,4}}
 I={{0,3},{1,6},{2,5},{7,4},{8,13},{9,12},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 6)(2 3 5)(4 7)(8 13)(9 12)(10 11)
      B_1={{0,5,6},{0,11,12},{0,13,4},{1,8,10},{1,12,4},{2,3,6},
      {2,8,11},{2,9,4},{3,8,9},{3,11,4},{5,8,4},{5,9,11},
      {6,8,12},{6,10,4}}
   B: \alpha=(0)(1 6)(2 5)(3)(4 7)(8 13)(9 12)(10 11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,11,13},
      {2,7,10},{2,12,13},{3,7,12},{3,10,13},{5,7,13},{5,10,12},
      {6,7,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 17 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=4 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,7,10},{2,8,11},{2,9,5},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,5},{4,7,5},{4,8,13},{4,9,12},{4,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,5}}
 I={{0,6},{1,3},{2,4},{7,13},{8,5},{9,11},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 3)(2 4)(5)(7 8 9 13 11 10 12)
      B_1={{0,3,4},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,5},
      {2,7,10},{2,8,11},{2,9,5},{2,12,13},{3,7,12},{3,8,9},
      {3,10,13},{3,11,5}}
   B: \alpha=(0)(1 3)(2 4)(5 7 9 12)(6)(8 13 11 10)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,5},{2,7,10},{2,8,11},{2,9,5},{2,12,13},
      {6,7,11},{6,8,12}}
   D: \alpha=(0 6)(1 2 3 4)(5)(7 12 13 10)(8)(9 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},
      {2,7,10},{2,8,11},{2,9,5},{2,12,13},{4,7,5},{4,8,13},
      {4,9,12},{4,10,11}}
 # of antimorphisms of SASC-graph: 618 (fair: 138) 
 # of halving permutations: 8 (fair: 8; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=4 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,5},{2,7,10},{2,8,11},{2,9,6},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,6},{4,7,6},{4,8,13},{4,9,12},{4,10,11},
 {5,7,13},{5,8,6},{5,9,11},{5,10,12}}
 I={{0,5},{1,4},{2,3},{7,11},{8,12},{9,13},{10,6}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 4)(2 3 5)(6 7 9 12)(8 10 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,6},{2,7,10},{2,12,13},{3,7,12},{3,10,13},
      {5,7,13},{5,10,12}}
   B: \alpha=(0)(1 4)(2 3)(5)(6 7 9 12)(8 10 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,6},{2,7,10},{2,8,11},{2,9,6},{2,12,13},
      {5,7,13},{5,10,12}}
 # of antimorphisms of SASC-graph: 355 (fair: 71) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,11},{2,9,7},{2,12,13},
 {3,8,9},{3,10,13},{3,11,7},{4,8,13},{4,9,12},{4,10,11},{5,8,7},{5,9,11},
 {5,10,12},{6,8,12},{6,9,13},{6,10,7}}
 I={{0,8},{1,9},{2,10},{3,12},{4,7},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 9 12 2 5 11)(4 7)(6 8 10 13)
      B_1={{0,1,2},{0,13,7},{1,8,10},{1,11,13},{1,12,7},{2,8,11},
      {2,9,7},{2,12,13},{3,8,9},{3,11,7},{4,8,13},{5,8,7},
      {5,9,11},{6,9,13}}
   B: \alpha=(0)(1 3 10 11)(2 6 9 12)(4 7)(5 13)(8)
      B_1={{0,1,2},{0,9,10},{0,13,7},{1,11,13},{1,12,7},{2,8,11},
      {2,9,7},{2,12,13},{3,8,9},{3,10,13},{3,11,7},{4,8,13},
      {6,9,13},{6,10,7}}
   C: \alpha=(0 2 3 7 13 12 10 1 5 8 4 9)(6 11)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,13,7},{1,3,5},{1,4,6},
      {2,3,6},{2,4,5},{3,10,13},{4,8,13},{5,10,12},{6,8,12},
      {6,9,13},{6,10,7}}
 # of antimorphisms of SASC-graph: 250 (fair: 24) 
 # of halving permutations: 18 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,9,8},{2,12,13},
 {3,7,12},{3,10,13},{3,11,8},{4,7,8},{4,9,12},{4,10,11},{5,7,13},{5,9,11},
 {5,10,12},{6,7,11},{6,9,13},{6,10,8}}
 I={{0,7},{1,10},{2,11},{3,9},{4,13},{5,8},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 9)(2 3 8 6 11 10 7 12)(4 13)
      B_1={{0,1,2},{0,13,8},{1,7,9},{1,11,13},{1,12,8},{2,7,10},
      {2,9,8},{2,12,13},{3,10,13},{3,11,8},{5,7,13},{5,9,11},
      {6,7,11},{6,9,13}}
   B: \alpha=(0 1 5 9)(2 6 11 12)(3 7 10 8)(4 13)
      B_1={{0,1,2},{0,13,8},{1,7,9},{1,11,13},{1,12,8},{2,7,10},
      {2,9,8},{2,12,13},{3,10,13},{3,11,8},{5,7,13},{5,9,11},
      {6,7,11},{6,9,13}}
   C: \alpha=(0 1 5 9)(2 6 7 3 11 12 8 10)(4 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,3,6},{2,4,5},{3,7,12},{4,7,8},{4,9,12},{4,10,11},
      {5,10,12},{6,10,8}}
 # of antimorphisms of SASC-graph: 92 (fair: 4) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 System No. 9 
 |Aut(S)|=2 


 Subsystem No. 0 
 |Aut(T)|=2 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,9},{3,10,13},{3,11,0},
 {4,7,0},{4,8,13},{4,9,11},{4,10,12},{5,7,13},{5,8,0},{5,9,12},{5,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5 2 6)(3 4)(7 9 10 11 8 12 13)
      B_1={{1,4,6},{2,4,5},{4,7,0},{4,8,13},{4,9,11},{4,10,12},
      {5,7,13},{5,8,0},{5,9,12},{5,10,11},{6,7,11},{6,8,12},
      {6,9,13},{6,10,0}}
   B: \alpha=(0)(1 5 2 6)(3 4)(7 11 8 12)(9 10)(13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},
      {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,9},
      {3,10,13},{3,11,0}}
   C: \alpha=(0)(1 5 2 6)(3 4)(7 11 13 8 9 10 12)
      B_1={{1,4,6},{2,4,5},{4,7,0},{4,8,13},{4,9,11},{4,10,12},
      {5,7,13},{5,8,0},{5,9,12},{5,10,11},{6,7,11},{6,8,12},
      {6,9,13},{6,10,0}}
 # of antimorphisms of SASC-graph: 246 (fair: 62) 
 # of halving permutations: 24 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,9},{3,10,13},{3,11,1},
 {4,7,1},{4,8,13},{4,9,11},{4,10,12},{5,7,13},{5,8,1},{5,9,12},{5,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 12 5 13 6 11 4)(2)(7 9)(8 10)
      B_1={{0,9,10},{0,11,12},{0,13,1},{2,8,11},{2,9,1},{2,12,13},
      {3,8,9},{3,11,1},{4,8,13},{4,9,11},{5,8,1},{5,9,12},
      {6,8,12},{6,9,13}}
   B: \alpha=(0)(1 4 13 5)(2)(3 12 6 11)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,5},{2,7,10},
      {3,7,12},{3,10,13},{4,7,1},{4,10,12},{5,7,13},{5,10,11},
      {6,7,11},{6,10,1}}
   C: \alpha=(0 4 2 6)(1 7 10 8 12 11 9)(3 5)(13)
      B_1={{0,5,6},{2,4,5},{4,7,1},{4,8,13},{4,9,11},{4,10,12},
      {5,7,13},{5,8,1},{5,9,12},{5,10,11},{6,7,11},{6,8,12},
      {6,9,13},{6,10,1}}
   D: \alpha=(0 6 2 4)(1)(3 5)(7 9)(8 13 10 11)(12)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},
      {2,7,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,9},
      {3,10,13},{3,11,1}}
 # of antimorphisms of SASC-graph: 264 (fair: 96) 
 # of halving permutations: 14 (fair: 6; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,9},{3,10,13},{3,11,2},
 {4,7,2},{4,8,13},{4,9,11},{4,10,12},{5,7,13},{5,8,2},{5,9,12},{5,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,2}}
 I={{0,1},{3,6},{4,5},{7,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 3 2 7)(1 4 11 10)(5 8 6 9)(12 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,13,2},{1,4,6},{1,11,13},
      {3,10,13},{4,7,2},{4,8,13},{5,7,13},{5,8,2},{5,10,11},
      {6,9,13},{6,10,2}}
   C: \alpha=(0 2 5 11 6 13 8 3)(1 12 9 4)(7 10)
      B_1={{0,9,10},{0,13,2},{1,3,5},{1,8,10},{1,11,13},{1,12,2},
      {3,8,9},{3,10,13},{3,11,2},{4,9,11},{4,10,12},{5,10,11},
      {6,9,13},{6,10,2}}
 # of antimorphisms of SASC-graph: 16 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=2 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,11},{2,9,3},{2,12,13},
 {4,7,3},{4,8,13},{4,9,11},{4,10,12},{5,7,13},{5,8,3},{5,9,12},{5,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,3}}
 I={{0,4},{1,5},{2,6},{7,12},{8,9},{10,13},{11,3}}
 Examples of antimorphisms:
   A: \alpha=(0 3 6 9)(1 2 8 12)(4 11 7 5)(10 13)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,4,6},
      {1,8,10},{2,4,5},{2,7,10},{4,10,12},{5,10,11},{6,7,11},
      {6,8,12},{6,10,3}}
   C: \alpha=(0 1 10 6 9 4 2 8 3 13 11 5)(7 12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,13,3},{1,7,9},{2,7,10},
      {2,8,11},{2,9,3},{4,7,3},{4,9,11},{5,7,13},{5,10,11},
      {6,7,11},{6,10,3}}
 # of antimorphisms of SASC-graph: 40 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=2 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,10},{2,8,11},{2,9,4},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,4},{5,7,13},{5,8,4},{5,9,12},{5,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,4}}
 I={{0,3},{1,6},{2,5},{7,4},{8,13},{9,11},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 9 4)(2 7 3 13)(5 6 11 8)(10 12)
      B_1={{0,7,8},{0,13,4},{1,7,9},{1,8,10},{1,11,13},{1,12,4},
      {2,12,13},{3,7,12},{5,7,13},{5,8,4},{6,7,11},{6,8,12},
      {6,9,13},{6,10,4}}
   C: \alpha=(0 1 4 2 12 9 13 5 6 8 3 10 11 7)
      B_1={{0,1,2},{0,9,10},{1,3,5},{1,7,9},{1,8,10},{2,7,10},
      {2,8,11},{2,9,4},{3,10,13},{5,7,13},{5,8,4},{5,9,12},
      {6,7,11},{6,8,12}}
 # of antimorphisms of SASC-graph: 88 (fair: 0) 
 # of halving permutations: 24 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,7,10},{2,8,11},{2,9,5},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,5},{4,7,5},{4,8,13},{4,9,11},{4,10,12},
 {6,7,11},{6,8,12},{6,9,13},{6,10,5}}
 I={{0,6},{1,3},{2,4},{7,13},{8,5},{9,12},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 9 13)(2 7 6 5)(3 12 8 4)(10 11)
      B_1={{0,13,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,5},
      {2,7,10},{2,12,13},{3,7,12},{3,10,13},{4,7,5},{4,8,13},
      {4,10,12},{6,10,5}}
   C: \alpha=(0 1 10 5)(2 11 7 4 3 8 6 13)(9 12)
      B_1={{0,13,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,5},
      {2,8,11},{2,9,5},{3,8,9},{3,11,5},{4,7,5},{4,8,13},
      {4,9,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 24 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,5},{2,7,10},{2,8,11},{2,9,6},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,6},{4,7,6},{4,8,13},{4,9,11},{4,10,12},
 {5,7,13},{5,8,6},{5,9,12},{5,10,11}}
 I={{0,5},{1,4},{2,3},{7,11},{8,12},{9,13},{10,6}}
 Examples of antimorphisms:
   A: \alpha=(0 4 5)(1)(2 3)(6 10)(7 11)(8 12)(9 13)
      B_1={{0,3,4},{0,9,10},{0,11,12},{1,3,5},{1,11,13},{1,12,6},
      {3,7,12},{3,8,9},{3,10,13},{3,11,6},{4,9,11},{4,10,12},
      {5,9,12},{5,10,11}}
   B: \alpha=(0 5)(1)(2 3)(4)(6 9 8 11)(7 10 13 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},
      {1,7,9},{1,11,13},{2,7,10},{2,8,11},{2,9,6},{2,12,13},
      {4,9,11},{4,10,12}}
   C: \alpha=(0 4 5)(1)(2 3)(6 9 8 11)(7 10 13 12)
      B_1={{0,3,4},{0,9,10},{0,11,12},{1,3,5},{1,8,10},{1,12,6},
      {3,7,12},{3,8,9},{3,10,13},{3,11,6},{4,9,11},{4,10,12},
      {5,9,12},{5,10,11}}
 # of antimorphisms of SASC-graph: 169 (fair: 35) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,11},{2,9,7},{2,12,13},
 {3,8,9},{3,10,13},{3,11,7},{4,8,13},{4,9,11},{4,10,12},{5,8,7},{5,9,12},
 {5,10,11},{6,8,12},{6,9,13},{6,10,7}}
 I={{0,8},{1,9},{2,10},{3,12},{4,7},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 10 11)(2 6 9 12)(4 7 8)(5 13)
      B_1={{0,3,4},{0,5,6},{0,11,12},{1,11,13},{2,3,6},{2,4,5},
      {2,8,11},{2,9,7},{3,8,9},{3,10,13},{3,11,7},{4,9,11},
      {5,8,7},{5,9,12}}
   B: \alpha=(0)(1 3 10 11)(2 6 9 12)(4 7)(5 13)(8)
      B_1={{0,1,2},{0,9,10},{0,13,7},{1,3,5},{1,4,6},{1,8,10},
      {1,12,7},{2,12,13},{4,8,13},{4,10,12},{5,10,11},{6,8,12},
      {6,9,13},{6,10,7}}
   C: \alpha=(0 4 1 12)(2 10)(3 8 13 11)(5 6 7 9)
      B_1={{0,9,10},{0,11,12},{1,4,6},{1,8,10},{3,10,13},{3,11,7},
      {4,8,13},{4,9,11},{4,10,12},{5,8,7},{5,9,12},{5,10,11},
      {6,8,12},{6,10,7}}
 # of antimorphisms of SASC-graph: 67 (fair: 5) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,9,8},{2,12,13},
 {3,7,12},{3,10,13},{3,11,8},{4,7,8},{4,9,11},{4,10,12},{5,7,13},{5,9,12},
 {5,10,11},{6,7,11},{6,9,13},{6,10,8}}
 I={{0,7},{1,10},{2,11},{3,9},{4,13},{5,8},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 8 9)(2 7 13 11 3 12)(4 6 10 5)
      B_1={{0,9,10},{0,11,12},{1,4,6},{1,7,9},{1,11,13},{1,12,8},
      {2,7,10},{3,7,12},{4,7,8},{4,9,11},{4,10,12},{5,9,12},
      {5,10,11},{6,7,11}}
   B: \alpha=(0 1 9 5)(2 13 11 4)(3 8 7 10)(6 12)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,8},{1,12,8},{2,7,10},
      {2,9,8},{2,12,13},{3,7,12},{3,11,8},{4,9,11},{4,10,12},
      {5,9,12},{5,10,11}}
   C: \alpha=(0 1 11 4 2 13 9 5)(3 8 7 10)(6 12)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,8},{1,12,8},{2,7,10},
      {2,9,8},{2,12,13},{3,7,12},{3,11,8},{4,9,11},{4,10,12},
      {5,9,12},{5,10,11}}
 # of antimorphisms of SASC-graph: 54 (fair: 2) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,5},{2,7,10},{2,8,11},{2,12,13},
 {3,7,12},{3,10,13},{3,11,9},{4,7,9},{4,8,13},{4,10,12},{5,7,13},{5,8,9},
 {5,10,11},{6,7,11},{6,8,12},{6,10,9}}
 I={{0,10},{1,7},{2,9},{3,8},{4,11},{5,12},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 8 4)(2 10 11 12 9 3 7 5)(6 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{0,13,9},{1,11,13},{2,7,10},
      {2,8,11},{2,12,13},{3,10,13},{3,11,9},{4,7,9},{4,8,13},
      {5,7,13},{5,8,9}}
   B: \alpha=(0 1 8 4)(2 12 9 5)(3 11 10 7)(6 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{0,13,9},{1,11,13},{2,7,10},
      {2,8,11},{2,12,13},{3,10,13},{3,11,9},{4,7,9},{4,8,13},
      {5,7,13},{5,8,9}}
   D: \alpha=(0 13 12 1)(2 9)(3 8)(4)(5 7 10 6)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{2,3,6},
      {2,4,5},{2,7,10},{2,8,11},{2,12,13},{3,7,12},{4,10,12},
      {5,10,11},{6,8,12}}
 # of antimorphisms of SASC-graph: 100 (fair: 14) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,5},{2,8,11},{2,9,10},{2,12,13},
 {3,7,12},{3,8,9},{3,11,10},{4,7,10},{4,8,13},{4,9,11},{5,7,13},{5,8,10},
 {5,9,12},{6,7,11},{6,8,12},{6,9,13}}
 I={{0,9},{1,8},{2,7},{3,13},{4,12},{5,11},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 10)(2 7)(4 5 9 8)(6 12 11 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,4,6},{2,3,6},
      {2,4,5},{2,8,11},{2,9,10},{2,12,13},{3,8,9},{3,11,10},
      {4,9,11},{6,9,13}}
   B: \alpha=(0)(1 3 7 10)(2 6 8 13)(4 12)(5 11)(9)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,11,13},{1,12,10},{2,8,11},
      {2,9,10},{2,12,13},{3,7,12},{3,8,9},{3,11,10},{4,9,11},
      {6,7,11},{6,8,12}}
   C: \alpha=(0 1 9 10 4 5 3 8)(2 7)(6 12 11 13)
      B_1={{0,7,8},{0,13,10},{1,3,5},{1,7,9},{1,11,13},{1,12,10},
      {3,7,12},{4,7,10},{4,8,13},{5,7,13},{5,8,10},{5,9,12},
      {6,7,11},{6,8,12}}
 # of antimorphisms of SASC-graph: 130 (fair: 34) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 System No. 10 
 |Aut(S)|=2 


 Subsystem No. 0 
 |Aut(T)|=2 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,9},{3,10,13},{3,11,0},
 {4,7,0},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,12},{5,9,11},{5,10,0},
 {6,7,11},{6,8,0},{6,9,13},{6,10,12}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5 2 6)(3 4)(7 9 10 11 8 12 13)
      B_1={{1,4,6},{2,4,5},{4,7,0},{4,8,13},{4,9,12},{4,10,11},
      {5,7,13},{5,8,12},{5,9,11},{5,10,0},{6,7,11},{6,8,0},
      {6,9,13},{6,10,12}}
   B: \alpha=(0)(1 5 2 6)(3 4)(7 11 8 12)(9 10)(13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},
      {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,9},
      {3,10,13},{3,11,0}}
 # of antimorphisms of SASC-graph: 164 (fair: 32) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,9},{3,10,13},{3,11,1},
 {4,7,1},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,12},{5,9,11},{5,10,1},
 {6,7,11},{6,8,1},{6,9,13},{6,10,12}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 2)(1 7 10 9 8 13 12 11)(3 4 5 6)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {4,7,1},{4,8,13},{4,9,12},{4,10,11},{6,7,11},{6,8,1},
      {6,9,13},{6,10,12}}
   B: \alpha=(0)(1 7 11 10)(2)(3 5)(4 6)(8 12 9 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,6},{2,7,10},{2,12,13},
      {5,7,13},{5,8,12},{5,9,11},{5,10,1},{6,7,11},{6,8,1},
      {6,9,13},{6,10,12}}
   C: \alpha=(0 2)(1 7 12 9 8 13 10 11)(3 4 5 6)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {3,7,12},{3,8,9},{3,10,13},{3,11,1},{5,7,13},{5,8,12},
      {5,9,11},{5,10,1}}
 # of antimorphisms of SASC-graph: 242 (fair: 62) 
 # of halving permutations: 24 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,9},{3,10,13},{3,11,2},
 {4,7,2},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,12},{5,9,11},{5,10,2},
 {6,7,11},{6,8,2},{6,9,13},{6,10,12}}
 I={{0,1},{3,6},{4,5},{7,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 1 9 4 8 5 11)(3)(6)(7 10)(12 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {1,8,10},{1,12,2},{3,7,12},{4,9,12},{4,10,11},{5,8,12},
      {5,10,2},{6,10,12}}
   B: \alpha=(0 1)(2 9)(3)(4 5)(6)(7 10)(8 11)(12 13)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {3,7,12},{3,8,9},{5,7,13},{5,8,12},{5,9,11},{5,10,2},
      {6,7,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 53 (fair: 21) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=2 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,11},{2,9,3},{2,12,13},
 {4,7,3},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,12},{5,9,11},{5,10,3},
 {6,7,11},{6,8,3},{6,9,13},{6,10,12}}
 I={{0,4},{1,5},{2,6},{7,12},{8,9},{10,13},{11,3}}
 Examples of antimorphisms:
   A: \alpha=(0 3 4 11)(1 8 13 7 10 12 5 9)(2 6)
      B_1={{0,5,6},{0,13,3},{1,4,6},{1,8,10},{1,11,13},{1,12,3},
      {4,10,11},{5,7,13},{5,9,11},{5,10,3},{6,7,11},{6,8,3},
      {6,9,13},{6,10,12}}
   B: \alpha=(0 3 4 11)(1 8 5 9)(2 6)(7 10 12 13)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,4,6},
      {1,7,9},{2,4,5},{2,7,10},{2,12,13},{4,7,3},{4,8,13},
      {4,9,12},{5,8,12}}
   C: \alpha=(0 3 4 11)(1 8 5 7 10 12 13 9)(2 6)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{1,7,9},{2,4,5},
      {2,7,10},{2,8,11},{2,9,3},{2,12,13},{4,7,3},{4,8,13},
      {4,9,12},{5,8,12}}
 # of antimorphisms of SASC-graph: 93 (fair: 43) 
 # of halving permutations: 10 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=2 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,10},{2,8,11},{2,9,4},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,4},{5,7,13},{5,8,12},{5,9,11},{5,10,4},
 {6,7,11},{6,8,4},{6,9,13},{6,10,12}}
 I={{0,3},{1,6},{2,5},{7,4},{8,13},{9,12},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 2 6 7)(1 4 11 9)(3 5 10 12)(8 13)
      B_1={{0,1,2},{0,5,6},{0,11,12},{0,13,4},{1,3,5},{1,11,13},
      {1,12,4},{2,12,13},{3,10,13},{5,7,13},{5,9,11},{6,7,11},
      {6,9,13},{6,10,12}}
   B: \alpha=(0 2 9 11)(1 8 6 13)(3 5 12 10)(4 7)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{1,3,5},{1,7,9},
      {1,8,10},{2,7,10},{3,7,12},{5,7,13},{5,9,11},{6,7,11},
      {6,9,13},{6,10,12}}
   C: \alpha=(0 1 7 12)(2 9 3 11)(4 8 5 6 13 10)
      B_1={{0,11,12},{0,13,4},{1,3,5},{1,7,9},{1,11,13},{1,12,4},
      {2,9,4},{2,12,13},{3,11,4},{5,7,13},{5,8,12},{5,9,11},
      {5,10,4},{6,9,13}}
 # of antimorphisms of SASC-graph: 68 (fair: 4) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,7,10},{2,8,11},{2,9,5},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,5},{4,7,5},{4,8,13},{4,9,12},{4,10,11},
 {6,7,11},{6,8,5},{6,9,13},{6,10,12}}
 I={{0,6},{1,3},{2,4},{7,13},{8,12},{9,11},{10,5}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,5},{2,7,10},{2,8,11},{2,9,6},{2,12,13},
 {3,7,12},{3,8,9},{3,10,13},{3,11,6},{4,7,6},{4,8,13},{4,9,12},{4,10,11},
 {5,7,13},{5,8,12},{5,9,11},{5,10,6}}
 I={{0,5},{1,4},{2,3},{7,11},{8,6},{9,13},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 7 4 13)(1 2 10 9 5 3 12 11)(6 8)
      B_1={{0,13,6},{1,7,9},{1,11,13},{2,7,10},{2,8,11},{2,9,6},
      {2,12,13},{3,7,12},{3,8,9},{3,10,13},{3,11,6},{4,7,6},
      {5,7,13},{5,9,11}}
   B: \alpha=(0)(1 4)(2 3)(5)(6 8)(7 11)(9 13)(10 12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,3,5},{1,8,10},{1,11,13},
      {2,7,10},{2,8,11},{3,8,9},{3,10,13},{4,8,13},{4,10,11},
      {5,7,13},{5,8,12}}
   C: \alpha=(0 7 4 13)(1 2 12 11)(3 10 9 5)(6 8)
      B_1={{0,13,6},{1,7,9},{1,11,13},{2,7,10},{2,8,11},{2,9,6},
      {2,12,13},{3,7,12},{3,10,13},{3,11,6},{4,7,6},{5,7,13},
      {5,9,11},{5,10,6}}
 # of antimorphisms of SASC-graph: 65 (fair: 1) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,11},{2,9,7},{2,12,13},
 {3,8,9},{3,10,13},{3,11,7},{4,8,13},{4,9,12},{4,10,11},{5,8,12},{5,9,11},
 {5,10,7},{6,8,7},{6,9,13},{6,10,12}}
 I={{0,8},{1,9},{2,10},{3,12},{4,7},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 11)(2 3 9 13)(4 8 10 7 6 12)
      B_1={{0,11,12},{0,13,7},{1,3,5},{1,8,10},{1,11,13},{1,12,7},
      {2,8,11},{2,9,7},{2,12,13},{3,8,9},{3,11,7},{4,9,12},
      {5,8,12},{6,8,7}}
   B: \alpha=(0 3 10 7)(1)(2 4 8 12)(5 13)(6 11)(9)
      B_1={{0,1,2},{0,11,12},{0,13,7},{1,8,10},{1,11,13},{2,4,5},
      {2,8,11},{2,9,7},{3,8,9},{3,10,13},{3,11,7},{4,10,11},
      {5,8,12},{5,9,11}}
   C: \alpha=(0 7 11 9 4 10)(1 8 13 3 5 12 2 6)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,7},{1,3,5},
      {1,4,6},{1,11,13},{2,4,5},{2,8,11},{2,12,13},{4,8,13},
      {4,10,11},{5,9,11}}
 # of antimorphisms of SASC-graph: 67 (fair: 5) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,9,8},{2,12,13},
 {3,7,12},{3,10,13},{3,11,8},{4,7,8},{4,9,12},{4,10,11},{5,7,13},{5,9,11},
 {5,10,8},{6,7,11},{6,9,13},{6,10,12}}
 I={{0,7},{1,10},{2,11},{3,9},{4,13},{5,12},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 7 3 11)(2 6 9 12 8 10)(4 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,3,6},{2,4,5},{3,7,12},{4,7,8},{4,9,12},{4,10,11},
      {5,10,8},{6,10,12}}
   B: \alpha=(0 1 6 9)(2 5 11 12)(3 7 10 8)(4 13)
      B_1={{0,1,2},{0,13,8},{1,7,9},{1,11,13},{1,12,8},{2,7,10},
      {2,9,8},{2,12,13},{3,10,13},{3,11,8},{5,7,13},{5,9,11},
      {6,7,11},{6,9,13}}
   C: \alpha=(0 1 6 9)(2 5 7 3 11 12 8 10)(4 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,3,6},{2,4,5},{3,7,12},{4,7,8},{4,9,12},{4,10,11},
      {5,10,8},{6,10,12}}
   D: \alpha=(0 7)(1 9 12 2)(3 5 11 10)(4 13)(6)(8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},
      {1,3,5},{1,4,6},{1,12,8},{2,4,5},{3,11,8},{4,9,12},
      {4,10,11},{6,10,12}}
 # of antimorphisms of SASC-graph: 150 (fair: 18) 
 # of halving permutations: 11 (fair: 1; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,5},{2,7,10},{2,8,11},{2,12,13},
 {3,7,12},{3,10,13},{3,11,9},{4,7,9},{4,8,13},{4,10,11},{5,7,13},{5,8,12},
 {5,10,9},{6,7,11},{6,8,9},{6,10,12}}
 I={{0,10},{1,7},{2,9},{3,8},{4,12},{5,11},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 8)(2 3 11 6 9 7 10 13)(4 12)
      B_1={{0,1,2},{0,11,12},{1,8,10},{1,11,13},{1,12,9},{2,7,10},
      {2,8,11},{2,12,13},{3,7,12},{3,11,9},{5,8,12},{5,10,9},
      {6,8,9},{6,10,12}}
   B: \alpha=(0 1 5 8)(2 6 9 13)(3 10 7 11)(4 12)
      B_1={{0,1,2},{0,11,12},{1,8,10},{1,11,13},{1,12,9},{2,7,10},
      {2,8,11},{2,12,13},{3,7,12},{3,11,9},{5,8,12},{5,10,9},
      {6,8,9},{6,10,12}}
   C: \alpha=(0 1 6 10 3 9 13 11 7 2 5 8)(4 12)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,13,9},{1,3,5},{1,4,6},
      {2,3,6},{2,4,5},{3,10,13},{4,7,9},{4,8,13},{4,10,11},
      {5,7,13},{6,7,11}}
 # of antimorphisms of SASC-graph: 60 (fair: 2) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,5},{2,8,11},{2,9,10},{2,12,13},
 {3,7,12},{3,8,9},{3,11,10},{4,7,10},{4,8,13},{4,9,12},{5,7,13},{5,8,12},
 {5,9,11},{6,7,11},{6,8,10},{6,9,13}}
 I={{0,9},{1,8},{2,7},{3,13},{4,11},{5,10},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 10 4 12)(2 5 8 7 9 11)(3 13)
      B_1={{0,1,2},{0,7,8},{0,13,10},{1,11,13},{1,12,10},{2,4,5},
      {2,12,13},{4,8,13},{4,9,12},{5,7,13},{5,9,11},{6,7,11},
      {6,8,10},{6,9,13}}
   B: \alpha=(0)(1 6 8 12)(2 4 7 11)(3 13)(5 10)(9)
      B_1={{0,1,2},{0,7,8},{0,13,10},{1,11,13},{1,12,10},{2,4,5},
      {2,12,13},{4,8,13},{4,9,12},{5,7,13},{5,9,11},{6,7,11},
      {6,8,10},{6,9,13}}
   C: \alpha=(0 2 6 9 1 3 11 12 13 7 4 8)(5 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,11,13},{2,4,5},{4,8,13},{5,7,13},{5,8,12},{5,9,11},
      {6,7,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 186 (fair: 36) 
 # of halving permutations: 14 (fair: 0; strong: 0) 


 System No. 11 
 |Aut(S)|=2 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,13},{3,9,11},{3,10,0},
 {4,7,0},{4,8,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,0},
 {6,7,11},{6,8,0},{6,9,12},{6,10,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 11 13 12)(1 2)(3 8 4 7 6 10 5 9)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,9,11},{3,10,0},{4,8,12},{4,9,13},{5,7,13},{5,10,12},
      {6,7,11},{6,8,0}}
   B: \alpha=(0)(1 2)(3 7 6 9)(4 8 5 10)(11 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,12},{3,8,13},{3,10,0},{4,8,12},{5,10,12},{6,8,0},
      {6,9,12},{6,10,13}}
 # of antimorphisms of SASC-graph: 17 (fair: 9) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,13},{3,9,11},{3,10,2},
 {4,7,2},{4,8,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,2},
 {6,7,11},{6,8,2},{6,9,12},{6,10,13}}
 I={{0,1},{3,6},{4,5},{7,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 4 9)(3 6)(5)(7 10)(8 11)(12 13)
      B_1={{0,7,8},{0,11,12},{1,3,5},{1,4,6},{1,7,9},{1,12,2},
      {4,7,2},{4,8,12},{5,8,9},{5,10,12},{6,7,11},{6,8,2},
      {6,9,12},{6,10,13}}
   B: \alpha=(0 1)(2 9)(3 6)(4)(5)(7 10)(8 11)(12 13)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,11,12},{1,7,9},{1,12,2},
      {3,7,12},{3,9,11},{4,7,2},{4,8,12},{5,7,13},{5,8,9},
      {6,7,11},{6,9,12}}
 # of antimorphisms of SASC-graph: 9 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,10},{2,8,11},{2,9,3},{2,12,13},
 {4,7,3},{4,8,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,3},
 {6,7,11},{6,8,3},{6,9,12},{6,10,13}}
 I={{0,4},{1,5},{2,6},{7,12},{8,13},{9,11},{10,3}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 7)(2 12 4 9)(5 10 11 6)(8 13)
      B_1={{0,7,8},{0,9,10},{1,4,6},{1,7,9},{1,8,10},{1,12,3},
      {2,7,10},{2,12,13},{4,9,13},{5,10,12},{6,7,11},{6,8,3},
      {6,9,12},{6,10,13}}
   C: \alpha=(0 3 9 8 13 2 5 1 10 6 12 4 11 7)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,8,10},{1,11,13},
      {2,9,3},{2,12,13},{4,9,13},{4,10,11},{5,7,13},{5,10,12},
      {5,11,3},{6,9,12}}
 # of antimorphisms of SASC-graph: 34 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=2 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,10},{2,8,11},{2,9,4},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,4},{5,7,13},{5,8,9},{5,10,12},{5,11,4},
 {6,7,11},{6,8,4},{6,9,12},{6,10,13}}
 I={{0,3},{1,6},{2,5},{7,4},{8,12},{9,13},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 6)(2 5)(4 7 9 8 12 13)(10)(11)
      B_1={{0,5,6},{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,4},
      {2,7,10},{2,8,11},{2,9,4},{2,12,13},{6,7,11},{6,8,4},
      {6,9,12},{6,10,13}}
   B: \alpha=(0 1 3 6)(2 5)(4 7)(8)(9 13)(10 11)(12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{2,3,6},
      {2,7,10},{2,8,11},{2,9,4},{2,12,13},{3,7,12},{3,8,13},
      {3,9,11},{3,10,4}}
   C: \alpha=(0 1 3 6)(2 5)(4 7 9 11 10 13)(8)(12)
      B_1={{0,5,6},{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,4},
      {5,7,13},{5,8,9},{5,10,12},{5,11,4},{6,7,11},{6,8,4},
      {6,9,12},{6,10,13}}
   D: \alpha=(0 1 3 6)(2 5)(4 7)(8 12)(9 13)(10 11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{2,3,6},
      {2,7,10},{2,8,11},{2,9,4},{2,12,13},{3,7,12},{3,8,13},
      {3,9,11},{3,10,4}}
 # of antimorphisms of SASC-graph: 71 (fair: 23) 
 # of halving permutations: 5 (fair: 1; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,7,10},{2,8,11},{2,9,5},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,5},{4,7,5},{4,8,12},{4,9,13},{4,10,11},
 {6,7,11},{6,8,5},{6,9,12},{6,10,13}}
 I={{0,6},{1,3},{2,4},{7,13},{8,9},{10,12},{11,5}}
 Examples of antimorphisms:
   B: \alpha=(0 5 1 9)(2 4)(3 8 6 11)(7 10 13 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{1,4,6},
      {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,7,10},{2,12,13},
      {3,8,13},{6,7,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,11},{2,9,7},{2,12,13},
 {3,8,13},{3,9,11},{3,10,7},{4,8,12},{4,9,13},{4,10,11},{5,8,9},{5,10,12},
 {5,11,7},{6,8,7},{6,9,12},{6,10,13}}
 I={{0,8},{1,9},{2,10},{3,12},{4,7},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 11)(2 5 9 12)(4 8 10 7 6 13)
      B_1={{0,11,12},{0,13,7},{1,3,5},{1,8,10},{1,11,13},{1,12,7},
      {2,8,11},{2,9,7},{2,12,13},{3,8,13},{4,9,13},{5,8,9},
      {5,11,7},{6,8,7}}
   B: \alpha=(0 2 13 4)(1 12 9 3)(5 7 8 10)(6 11)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,11,13},
      {1,12,7},{3,8,13},{3,9,11},{3,10,7},{4,9,13},{5,10,12},
      {6,8,7},{6,10,13}}
   C: \alpha=(0 1 12 4)(2 13 9 3)(5 7 8 10)(6 11)
      B_1={{0,3,4},{0,9,10},{1,4,6},{1,8,10},{1,11,13},{1,12,7},
      {2,4,5},{2,8,11},{2,9,7},{2,12,13},{3,9,11},{4,10,11},
      {5,8,9},{5,11,7}}
   D: \alpha=(0 4 13 2)(1 3 9 12)(5 10 8 7)(6 11)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,11,13},
      {1,12,7},{3,8,13},{3,9,11},{3,10,7},{4,9,13},{5,10,12},
      {6,8,7},{6,10,13}}
 # of antimorphisms of SASC-graph: 73 (fair: 9) 
 # of halving permutations: 9 (fair: 1; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,9,8},{2,12,13},
 {3,7,12},{3,9,11},{3,10,8},{4,7,8},{4,9,13},{4,10,11},{5,7,13},{5,10,12},
 {5,11,8},{6,7,11},{6,9,12},{6,10,13}}
 I={{0,7},{1,10},{2,11},{3,13},{4,12},{5,9},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 1 9 8)(2 12 10 13 4 7)(3 11 5 6)
      B_1={{0,1,2},{0,3,4},{0,9,10},{1,3,5},{1,4,6},{2,3,6},
      {2,4,5},{2,7,10},{2,9,8},{3,10,8},{4,9,13},{4,10,11},
      {5,10,12},{5,11,8}}
 # of antimorphisms of SASC-graph: 12 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,5},{2,7,10},{2,8,11},{2,12,13},
 {3,7,12},{3,8,13},{3,10,9},{4,7,9},{4,8,12},{4,10,11},{5,7,13},{5,10,12},
 {5,11,9},{6,7,11},{6,8,9},{6,10,13}}
 I={{0,10},{1,7},{2,9},{3,11},{4,13},{5,8},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 11 4)(2 13 10 8)(3 5 9 7)(6 12)
      B_1={{0,3,4},{0,7,8},{1,4,6},{1,8,10},{1,11,13},{1,12,9},
      {2,4,5},{2,7,10},{2,12,13},{3,7,12},{4,8,12},{5,7,13},
      {5,10,12},{5,11,9}}
   B: \alpha=(0 6 13 7)(1 10 12 4)(2 9)(3)(5 8)(11)
      B_1={{0,1,2},{0,5,6},{1,3,5},{1,4,6},{2,3,6},{2,4,5},
      {2,7,10},{2,8,11},{2,12,13},{3,7,12},{4,10,11},{5,7,13},
      {5,10,12},{6,7,11}}
 # of antimorphisms of SASC-graph: 8 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,5},{2,8,11},{2,9,10},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{4,7,10},{4,8,12},{4,9,13},{5,7,13},{5,8,9},
 {5,11,10},{6,7,11},{6,8,10},{6,9,12}}
 I={{0,9},{1,8},{2,7},{3,10},{4,11},{5,12},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 11)(2 3 8 12)(4 10 6 9 7 13)
      B_1={{0,1,2},{0,13,10},{1,7,9},{1,11,13},{1,12,10},{2,8,11},
      {2,9,10},{2,12,13},{3,8,13},{3,9,11},{4,9,13},{5,8,9},
      {5,11,10},{6,8,10}}
   B: \alpha=(0 3 9 10)(1 6 11 2)(4 7 8 13)(5 12)
      B_1={{0,1,2},{0,7,8},{0,11,12},{0,13,10},{1,7,9},{1,11,13},
      {1,12,10},{2,12,13},{3,7,12},{3,9,11},{4,8,12},{4,9,13},
      {6,7,11},{6,9,12}}
   C: \alpha=(0 2 12 9 7 5)(1 13 6)(3 10)(4 11)(8)
      B_1={{0,5,6},{1,3,5},{1,4,6},{1,7,9},{2,3,6},{2,4,5},
      {2,8,11},{2,9,10},{2,12,13},{3,8,13},{3,9,11},{4,9,13},
      {5,8,9},{5,11,10}}
 # of antimorphisms of SASC-graph: 57 (fair: 5) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 System No. 12 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,13},{3,9,11},{3,10,0},
 {4,7,0},{4,8,12},{4,9,13},{4,10,11},{5,7,11},{5,8,0},{5,9,12},{5,10,13},
 {6,7,13},{6,8,9},{6,10,12},{6,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 1 13)(2)(3 4)(5 6)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,8,10},{1,12,0},{2,3,6},{2,7,10},{2,12,13},
      {3,7,12},{3,8,13},{3,9,11},{3,10,0},{5,7,11},{5,8,0},
      {5,9,12},{5,10,13}}
   B: \alpha=(0)(1 2)(3 7 5 9)(4 8 6 10)(11 12)(13)
      B_1={{1,3,5},{1,4,6},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
      {3,7,12},{3,8,13},{3,10,0},{4,8,12},{5,8,0},{5,9,12},
      {5,10,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 35 (fair: 9) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,13},{3,9,11},{3,10,1},
 {4,7,1},{4,8,12},{4,9,13},{4,10,11},{5,7,11},{5,8,1},{5,9,12},{5,10,13},
 {6,7,13},{6,8,9},{6,10,12},{6,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 5)(2 12 4 11)(3 6 13 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{2,4,5},{2,7,10},
      {2,9,1},{2,12,13},{3,9,11},{4,7,1},{4,10,11},{6,7,13},
      {6,8,9},{6,10,12}}
   B: \alpha=(0)(1 12)(2)(3 7 4 8 5 9 6 10)(11 13)
      B_1={{0,3,4},{0,5,6},{0,11,12},{2,3,6},{2,4,5},{2,12,13},
      {3,7,12},{3,8,13},{4,8,12},{4,9,13},{5,9,12},{5,10,13},
      {6,7,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 12 (fair: 8) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=3 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,10},{2,8,11},{2,9,4},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,4},{5,7,11},{5,8,4},{5,9,12},{5,10,13},
 {6,7,13},{6,8,9},{6,10,12},{6,11,4}}
 I={{0,3},{1,6},{2,5},{7,4},{8,12},{9,13},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 6)(2 5)(4 7 9 11 10 13)(8)(12)
      B_1={{0,5,6},{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,4},
      {5,7,11},{5,8,4},{5,9,12},{5,10,13},{6,7,13},{6,8,9},
      {6,10,12},{6,11,4}}
   B: \alpha=(0 1 3 6)(2 5)(4 7)(8)(9 13)(10 11)(12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{2,3,6},
      {2,7,10},{2,8,11},{2,9,4},{2,12,13},{3,7,12},{3,8,13},
      {3,9,11},{3,10,4}}
   C: \alpha=(0 1 3 6)(2 5)(4 7 10 13 9 11)(8)(12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{2,3,6},
      {2,7,10},{2,8,11},{2,9,4},{2,12,13},{3,7,12},{3,8,13},
      {3,9,11},{3,10,4}}
   D: \alpha=(0 3)(1 5 6 2)(4 11 12 7 10 8)(9 13)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},
      {2,7,10},{2,8,11},{2,9,4},{2,12,13},{5,7,11},{5,8,4},
      {5,9,12},{5,10,13}}
 # of antimorphisms of SASC-graph: 330 (fair: 60) 
 # of halving permutations: 15 (fair: 3; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,11},{2,9,7},{2,12,13},
 {3,8,13},{3,9,11},{3,10,7},{4,8,12},{4,9,13},{4,10,11},{5,8,7},{5,9,12},
 {5,10,13},{6,8,9},{6,10,12},{6,11,7}}
 I={{0,8},{1,9},{2,10},{3,12},{4,7},{5,11},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 7)(2 13 9 11 6 8)(4 5 10 12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,4,6},{2,3,6},
      {2,4,5},{2,9,7},{2,12,13},{3,9,11},{3,10,7},{5,9,12},
      {6,8,9},{6,10,12}}
   B: \alpha=(0)(1 3 9 12)(2 4 10 7)(5 11)(6 13)(8)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,4,6},{1,8,10},
      {2,3,6},{2,8,11},{2,9,7},{4,10,11},{5,9,12},{6,8,9},
      {6,10,12},{6,11,7}}
   C: \alpha=(0 4 5 9)(1 10 3 2 12 8 7 11)(6 13)
      B_1={{0,9,10},{1,4,6},{1,8,10},{2,3,6},{2,4,5},{2,8,11},
      {2,9,7},{3,9,11},{4,8,12},{4,9,13},{4,10,11},{6,8,9},
      {6,10,12},{6,11,7}}
 # of antimorphisms of SASC-graph: 252 (fair: 36) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,9,8},{2,12,13},
 {3,7,12},{3,9,11},{3,10,8},{4,7,8},{4,9,13},{4,10,11},{5,7,11},{5,9,12},
 {5,10,13},{6,7,13},{6,10,12},{6,11,8}}
 I={{0,7},{1,10},{2,11},{3,13},{4,12},{5,8},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 11)(2 5 9 13)(4 12)(6 7 10 8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,4,6},{2,3,6},
      {2,4,5},{3,9,11},{3,10,8},{4,7,8},{4,9,13},{4,10,11},
      {5,10,13},{6,7,13}}
   B: \alpha=(0 7)(1 5 6 12)(2 13 11 3)(4 10 8 9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},
      {1,4,6},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,9,8},
      {4,10,11},{6,11,8}}
   C: \alpha=(0 7)(1 3 2 13 11 5 6 12)(4 10 8 9)
      B_1={{1,3,5},{1,7,9},{2,7,10},{2,12,13},{3,7,12},{3,9,11},
      {3,10,8},{4,7,8},{4,9,13},{5,7,11},{5,9,12},{5,10,13},
      {6,7,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 58 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,5},{2,7,10},{2,8,11},{2,12,13},
 {3,7,12},{3,8,13},{3,10,9},{4,7,9},{4,8,12},{4,10,11},{5,7,11},{5,8,9},
 {5,10,13},{6,7,13},{6,10,12},{6,11,9}}
 I={{0,10},{1,7},{2,9},{3,11},{4,13},{5,12},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 13)(2 10 6 9 7 12)(4 5 8 11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,4,6},{2,3,6},
      {2,4,5},{2,7,10},{2,8,11},{3,7,12},{3,8,13},{5,7,11},
      {6,7,13},{6,11,9}}
   B: \alpha=(0 2 10 9)(1 6 3 13)(4 7 8 11)(5 12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,3,5},{1,4,6},
      {1,8,10},{2,4,5},{3,8,13},{3,10,9},{4,8,12},{4,10,11},
      {5,8,9},{5,10,13}}
   D: \alpha=(0 10)(1 13 6 3)(2 5 9 12)(4 8 11 7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},
      {1,4,6},{1,11,13},{1,12,9},{2,3,6},{2,4,5},{2,8,11},
      {4,7,9},{6,11,9}}
 # of antimorphisms of SASC-graph: 105 (fair: 7) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,5},{2,7,10},{2,8,11},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{4,8,12},{4,9,13},{4,10,11},{5,7,11},{5,9,12},
 {5,10,13},{6,7,13},{6,8,9},{6,10,12}}
 I={{0,13},{1,12},{2,9},{3,10},{4,7},{5,8},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 13 
 |Aut(S)|=8 


 Subsystem No. 0 
 |Aut(T)|=8 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,0},{3,9,11},{3,10,13},
 {4,7,0},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,0},
 {6,7,11},{6,8,12},{6,9,13},{6,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 2 8 6 13 5)(3)(4)(9 10)(11 12)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,11,13},{2,3,6},{2,4,5},
      {2,8,11},{2,9,0},{3,9,11},{4,9,12},{5,8,9},{5,11,0},
      {6,7,11},{6,9,13}}
   B: \alpha=(0)(1 7 2 8)(3 12 4 11)(5 6)(9 10)(13)
      B_1={{1,3,5},{1,4,6},{1,8,10},{1,11,13},{2,3,6},{2,4,5},
      {2,7,10},{2,12,13},{3,8,0},{3,9,11},{4,7,0},{4,9,12},
      {6,9,13},{6,10,0}}
 # of antimorphisms of SASC-graph: 114 (fair: 50) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=4 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,1},{3,9,11},{3,10,13},
 {4,7,1},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,1},
 {6,7,11},{6,8,12},{6,9,13},{6,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 7 11 10)(2 3 5)(4 6)(8 12 9 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,4,5},{2,7,10},{2,12,13},
      {3,7,12},{3,10,13},{4,7,1},{4,8,13},{4,9,12},{4,10,11},
      {5,7,13},{5,10,12}}
   B: \alpha=(0)(1 7 11 10)(2)(3 5)(4 6)(8 12 9 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,6},{2,7,10},{2,12,13},
      {3,7,12},{3,10,13},{4,7,1},{4,8,13},{4,9,12},{4,10,11},
      {5,7,13},{5,10,12}}
 # of antimorphisms of SASC-graph: 17 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=4 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,2},{3,9,11},{3,10,13},
 {4,7,2},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,2},
 {6,7,11},{6,8,12},{6,9,13},{6,10,2}}
 I={{0,1},{3,6},{4,5},{7,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 7 9 10 8 13 11 12)(3 4 6 5)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {4,7,2},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,9},
      {5,10,12},{5,11,2}}
   B: \alpha=(0 1)(2 7 9 10)(3 4 6 5)(8 13 11 12)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {4,7,2},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,9},
      {5,10,12},{5,11,2}}
   C: \alpha=(0 3 2 7)(1 5 11 10)(4 8 6 9)(12 13)
      B_1={{0,3,4},{0,5,6},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
      {1,11,13},{1,12,2},{4,7,2},{4,8,13},{4,10,11},{6,7,11},
      {6,9,13},{6,10,2}}
   D: \alpha=(0 1)(2 7 11 12)(3 4 6 5)(8 13 9 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {4,7,2},{4,8,13},{4,9,12},{4,10,11},{5,7,13},{5,8,9},
      {5,10,12},{5,11,2}}
 # of antimorphisms of SASC-graph: 112 (fair: 16) 
 # of halving permutations: 12 (fair: 4; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=8 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,7,10},{2,8,11},{2,9,5},{2,12,13},
 {3,7,12},{3,8,5},{3,9,11},{3,10,13},{4,7,5},{4,8,13},{4,9,12},{4,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,5}}
 I={{0,6},{1,3},{2,4},{7,13},{8,9},{10,12},{11,5}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 3)(2 4)(5 7 8 10 9 12 11 13)
      B_1={{0,3,4},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,5},
      {3,7,12},{3,8,5},{3,9,11},{3,10,13},{4,7,5},{4,8,13},
      {4,9,12},{4,10,11}}
   B: \alpha=(0)(1 3)(2 4)(5 7 9 12)(6)(8 10 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,5},{2,7,10},{2,8,11},{2,9,5},{2,12,13},
      {6,7,11},{6,8,12}}
 # of antimorphisms of SASC-graph: 102 (fair: 38) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=8 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,5},{2,7,10},{2,8,11},{2,9,6},{2,12,13},
 {3,7,12},{3,8,6},{3,9,11},{3,10,13},{4,7,6},{4,8,13},{4,9,12},{4,10,11},
 {5,7,13},{5,8,9},{5,10,12},{5,11,6}}
 I={{0,5},{1,4},{2,3},{7,11},{8,12},{9,13},{10,6}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 4)(2 3 5)(6 7 9 12)(8 10 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,6},{2,7,10},{2,12,13},{3,7,12},{3,10,13},
      {5,7,13},{5,10,12}}
   B: \alpha=(0)(1 4)(2 3)(5)(6 10)(7 11)(8 12)(9 13)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,12,6},
      {2,7,10},{2,8,11},{2,9,6},{2,12,13},{4,7,6},{4,9,12},
      {5,7,13},{5,10,12}}
   E: \alpha=(0)(1 4)(2 3)(5)(6 7 9 12)(8 10 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,6},{2,7,10},{2,8,11},{2,9,6},{2,12,13},
      {5,7,13},{5,10,12}}
 # of antimorphisms of SASC-graph: 65 (fair: 3) 
 # of halving permutations: 2 (fair: 2; strong: 2) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,11},{2,9,7},{2,12,13},
 {3,8,7},{3,9,11},{3,10,13},{4,8,13},{4,9,12},{4,10,11},{5,8,9},{5,10,12},
 {5,11,7},{6,8,12},{6,9,13},{6,10,7}}
 I={{0,8},{1,9},{2,10},{3,12},{4,7},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 9 12 2 5 11)(4 7)(6 8 10 13)
      B_1={{0,1,2},{0,13,7},{1,8,10},{1,11,13},{1,12,7},{2,8,11},
      {2,9,7},{2,12,13},{3,8,7},{3,9,11},{4,8,13},{5,8,9},
      {5,11,7},{6,9,13}}
   B: \alpha=(0 2 3 7)(1 5 9 13)(4 8 10 12)(6 11)
      B_1={{0,1,2},{0,11,12},{1,8,10},{1,11,13},{1,12,7},{2,8,11},
      {2,9,7},{2,12,13},{3,8,7},{3,9,11},{4,9,12},{4,10,11},
      {5,8,9},{5,11,7}}
   C: \alpha=(0 2 5 8 4 9)(1 3 7 13 12 10)(6 11)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,13,7},{1,3,5},{1,4,6},
      {2,3,6},{2,4,5},{3,10,13},{4,8,13},{5,10,12},{6,8,12},
      {6,9,13},{6,10,7}}
   D: \alpha=(0 11 5 2)(1 12 9 3)(4 7)(6 13 10 8)
      B_1={{0,1,2},{0,13,7},{1,8,10},{1,11,13},{1,12,7},{2,8,11},
      {2,9,7},{2,12,13},{3,8,7},{3,9,11},{4,8,13},{5,8,9},
      {5,11,7},{6,9,13}}
 # of antimorphisms of SASC-graph: 156 (fair: 16) 
 # of halving permutations: 7 (fair: 3; strong: 0) 


 System No. 14 
 |Aut(S)|=12 


 Subsystem No. 0 
 |Aut(T)|=4 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,0},{3,9,11},{3,10,13},
 {4,7,13},{4,8,9},{4,10,12},{4,11,0},{5,7,0},{5,8,13},{5,9,12},{5,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 11)(2 6 7 13)(4 12 5 8)(9 10)
      B_1={{1,7,9},{1,12,0},{2,3,6},{2,4,5},{2,8,11},{2,9,0},
      {3,7,12},{3,8,0},{3,9,11},{4,7,13},{4,8,9},{5,7,0},
      {5,9,12},{6,9,13}}
   B: \alpha=(0 7 11 10)(1)(2)(3 4)(5 6)(8 12 9 13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{2,3,6},{2,7,10},{2,12,13},
      {3,7,12},{3,10,13},{4,7,13},{4,10,12},{5,7,0},{5,8,13},
      {5,9,12},{5,10,11}}
 # of antimorphisms of SASC-graph: 49 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=12 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,1},{3,9,11},{3,10,13},
 {4,7,13},{4,8,9},{4,10,12},{4,11,1},{5,7,1},{5,8,13},{5,9,12},{5,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 12 5 11 4 13 6)(2)(7 9)(8 10)
      B_1={{0,9,10},{0,11,12},{0,13,1},{2,8,11},{2,9,1},{2,12,13},
      {3,8,1},{3,9,11},{4,8,9},{4,11,1},{5,8,13},{5,9,12},
      {6,8,12},{6,9,13}}
   B: \alpha=(0)(1 3 12 5)(2)(4 13 6 11)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,5},{2,7,10},
      {3,7,12},{3,10,13},{4,7,13},{4,10,12},{5,7,1},{5,10,11},
      {6,7,11},{6,10,1}}
 # of antimorphisms of SASC-graph: 144 (fair: 48) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=4 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,2},{3,9,11},{3,10,13},
 {4,7,13},{4,8,9},{4,10,12},{4,11,2},{5,7,2},{5,8,13},{5,9,12},{5,10,11},
 {6,7,11},{6,8,12},{6,9,13},{6,10,2}}
 I={{0,1},{3,6},{4,5},{7,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 7 9 10 8 13 11 12)(3 4 6 5)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {4,7,13},{4,8,9},{4,10,12},{4,11,2},{5,7,2},{5,8,13},
      {5,9,12},{5,10,11}}
   B: \alpha=(0 1)(2 7 9 10)(3 4 6 5)(8 13 11 12)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {4,7,13},{4,8,9},{4,10,12},{4,11,2},{5,7,2},{5,8,13},
      {5,9,12},{5,10,11}}
   C: \alpha=(0 4 2 10 1 3 11 7)(5 9 6 8)(12 13)
      B_1={{0,3,4},{0,5,6},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
      {1,11,13},{1,12,2},{5,7,2},{5,8,13},{5,10,11},{6,7,11},
      {6,9,13},{6,10,2}}
   D: \alpha=(0 1)(2 7 11 12)(3 5 6 4)(8 13 9 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {4,7,13},{4,8,9},{4,10,12},{4,11,2},{5,7,2},{5,8,13},
      {5,9,12},{5,10,11}}
 # of antimorphisms of SASC-graph: 112 (fair: 16) 
 # of halving permutations: 12 (fair: 4; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,11},{2,9,7},{2,12,13},
 {3,8,7},{3,9,11},{3,10,13},{4,8,9},{4,10,12},{4,11,7},{5,8,13},{5,9,12},
 {5,10,11},{6,8,12},{6,9,13},{6,10,7}}
 I={{0,8},{1,9},{2,10},{3,12},{4,13},{5,7},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 9 12 2 4 11)(5 7)(6 8 10 13)
      B_1={{0,1,2},{0,13,7},{1,8,10},{1,11,13},{1,12,7},{2,8,11},
      {2,9,7},{2,12,13},{3,8,7},{3,9,11},{4,8,9},{4,11,7},
      {5,8,13},{6,9,13}}
   B: \alpha=(0 2 3 7)(1 4 9 13)(5 8 10 12)(6 11)
      B_1={{0,1,2},{0,11,12},{1,8,10},{1,11,13},{1,12,7},{2,8,11},
      {2,9,7},{2,12,13},{3,8,7},{3,9,11},{4,8,9},{4,11,7},
      {5,9,12},{5,10,11}}
   C: \alpha=(0 2 4 9 13 1 3 7)(5 8 10 12)(6 11)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,13,7},{1,3,5},{1,4,6},
      {2,3,6},{2,4,5},{3,10,13},{4,10,12},{5,8,13},{6,8,12},
      {6,9,13},{6,10,7}}
 # of antimorphisms of SASC-graph: 432 (fair: 48) 
 # of halving permutations: 18 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,9,8},{2,12,13},
 {3,7,12},{3,9,11},{3,10,13},{4,7,13},{4,10,12},{4,11,8},{5,7,8},{5,9,12},
 {5,10,11},{6,7,11},{6,9,13},{6,10,8}}
 I={{0,7},{1,10},{2,11},{3,8},{4,9},{5,13},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 7 10 13)(2 3 8)(4 9)(6 12)(11)
      B_1={{0,13,8},{1,3,5},{1,4,6},{1,7,9},{1,11,13},{1,12,8},
      {2,7,10},{2,9,8},{2,12,13},{3,7,12},{3,9,11},{4,7,13},
      {6,7,11},{6,9,13}}
   B: \alpha=(0 1 13 12)(2 11)(3 8)(4)(5 6 7 10)(9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,13,8},{2,3,6},
      {2,4,5},{2,7,10},{2,9,8},{2,12,13},{3,10,13},{4,7,13},
      {6,9,13},{6,10,8}}
 # of antimorphisms of SASC-graph: 57 (fair: 9) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 15 
 |Aut(S)|=4 


 Subsystem No. 0 
 |Aut(T)|=4 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,11},{2,8,12},{2,9,13},{2,10,0},{3,7,0},{3,8,9},{3,10,11},{3,12,13},
 {4,7,13},{4,8,11},{4,9,0},{4,10,12},{5,7,10},{5,8,13},{5,9,12},{5,11,0},
 {6,7,12},{6,8,0},{6,9,11},{6,10,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 8 11 9)(1)(2)(3 4)(5 6)(7 12 10 13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{2,3,6},{2,7,11},{2,10,0},
      {3,7,0},{3,8,9},{3,10,11},{3,12,13},{6,7,12},{6,8,0},
      {6,9,11},{6,10,13}}
 # of antimorphisms of SASC-graph: 5 (fair: 5) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=4 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,11},{2,8,12},{2,9,13},{2,10,1},{3,7,1},{3,8,9},{3,10,11},{3,12,13},
 {4,7,13},{4,8,11},{4,9,1},{4,10,12},{5,7,10},{5,8,13},{5,9,12},{5,11,1},
 {6,7,12},{6,8,1},{6,9,11},{6,10,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 8 11 9)(2 3 5)(4 6)(7 12 10 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,4,5},{2,7,11},{2,10,1},
      {3,7,1},{3,10,11},{4,7,13},{4,8,11},{4,9,1},{4,10,12},
      {5,7,10},{5,11,1}}
   B: \alpha=(0)(1 8 11 9)(2)(3 5)(4 6)(7 12 10 13)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,6},{2,7,11},{2,10,1},
      {3,7,1},{3,8,9},{3,10,11},{3,12,13},{4,7,13},{4,8,11},
      {4,9,1},{4,10,12}}
   C: \alpha=(0 1 7 2 9 12)(3 4 6 5 11 13)(8 10)
      B_1={{0,5,6},{0,7,8},{0,13,1},{2,4,5},{2,7,11},{2,8,12},
      {3,8,9},{3,12,13},{4,7,13},{4,8,11},{4,9,1},{5,8,13},
      {5,9,12},{6,8,1}}
   D: \alpha=(0 2)(1)(3 4 5 6)(7 9)(8 13 10 11)(12)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {3,7,1},{3,8,9},{3,10,11},{3,12,13},{5,7,10},{5,8,13},
      {5,9,12},{5,11,1}}
   E: \alpha=(0)(1 12)(2)(3 5)(4 6)(7 9)(8 10)(11 13)
      B_1={{0,3,4},{0,7,8},{0,11,12},{2,3,6},{2,7,11},{2,8,12},
      {3,7,1},{3,8,9},{3,10,11},{3,12,13},{4,7,13},{4,8,11},
      {4,9,1},{4,10,12}}
 # of antimorphisms of SASC-graph: 251 (fair: 73) 
 # of halving permutations: 33 (fair: 13; strong: 1) 


 Subsystem No. 2 
 |Aut(T)|=4 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,2},{3,8,9},{3,10,11},{3,12,13},
 {4,7,13},{4,8,11},{4,9,2},{4,10,12},{5,7,10},{5,8,13},{5,9,12},{5,11,2},
 {6,7,12},{6,8,2},{6,9,11},{6,10,13}}
 I={{0,1},{3,6},{4,5},{7,11},{8,12},{9,13},{10,2}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 8 7 12 11 9 10 13)(3 4 6 5)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {4,7,13},{4,8,11},{4,9,2},{4,10,12},{5,7,10},{5,8,13},
      {5,9,12},{5,11,2}}
   B: \alpha=(0)(1)(2 8 11 9)(3 6)(4 5)(7 13 10 12)
      B_1={{0,3,4},{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,8,10},
      {3,7,2},{3,8,9},{3,10,11},{3,12,13},{4,7,13},{4,8,11},
      {4,9,2},{4,10,12}}
   D: \alpha=(0 1)(2 8 11 9)(3 5 6 4)(7 13 10 12)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {3,7,2},{3,8,9},{3,10,11},{3,12,13},{6,7,12},{6,8,2},
      {6,9,11},{6,10,13}}
 # of antimorphisms of SASC-graph: 118 (fair: 38) 
 # of halving permutations: 2 (fair: 2; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=2 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,11},{2,8,12},{2,9,13},{2,10,3},
 {4,7,13},{4,8,11},{4,9,3},{4,10,12},{5,7,10},{5,8,13},{5,9,12},{5,11,3},
 {6,7,12},{6,8,3},{6,9,11},{6,10,13}}
 I={{0,4},{1,5},{2,6},{7,3},{8,9},{10,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=2 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,11},{2,8,12},{2,9,13},{2,10,4},
 {3,7,4},{3,8,9},{3,10,11},{3,12,13},{5,7,10},{5,8,13},{5,9,12},{5,11,4},
 {6,7,12},{6,8,4},{6,9,11},{6,10,13}}
 I={{0,3},{1,6},{2,5},{7,13},{8,11},{9,4},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 5 4 10)(1 11 2 9)(3 6 8 12)(7 13)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,13,4},{1,3,5},{1,7,9},
      {1,8,10},{1,12,4},{2,3,6},{2,7,11},{2,8,12},{2,10,4},
      {3,7,4},{6,7,12}}
 # of antimorphisms of SASC-graph: 16 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,12},{2,9,13},{2,10,7},
 {3,8,9},{3,10,11},{3,12,13},{4,8,11},{4,9,7},{4,10,12},{5,8,13},{5,9,12},
 {5,11,7},{6,8,7},{6,9,11},{6,10,13}}
 I={{0,8},{1,9},{2,11},{3,7},{4,13},{5,10},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 10 2 8 7 13 11)(3 5 9 4)(6 12)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,7},{1,8,10},{1,12,7},
      {2,8,12},{2,9,13},{3,8,9},{3,10,11},{3,12,13},{4,10,12},
      {5,8,13},{5,9,12}}
   B: \alpha=(0 2 8 11)(1 13 7 10)(3 5 9 4)(6 12)
      B_1={{0,1,2},{0,5,6},{0,13,7},{1,3,5},{1,4,6},{1,8,10},
      {1,12,7},{2,3,6},{2,4,5},{4,8,11},{4,9,7},{5,11,7},
      {6,8,7},{6,9,11}}
   C: \alpha=(0 2 3 12 10 1 5 9)(4 8 6 13 11 7)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,3,6},{2,4,5},{3,10,11},{4,8,11},{4,10,12},{5,11,7},
      {6,9,11},{6,10,13}}
 # of antimorphisms of SASC-graph: 72 (fair: 4) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,5},{2,8,12},{2,9,13},{2,10,11},
 {3,7,11},{3,8,9},{3,12,13},{4,7,13},{4,9,11},{4,10,12},{5,7,10},{5,8,13},
 {5,9,12},{6,7,12},{6,8,11},{6,10,13}}
 I={{0,12},{1,13},{2,7},{3,10},{4,8},{5,11},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0 2 3 8)(1 5 12 7)(4 13 11 10)(6 9)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,13,11},{1,3,5},{1,4,6},
      {1,12,11},{2,3,6},{2,4,5},{3,7,11},{4,10,12},{6,7,12},
      {6,8,11},{6,10,13}}
   B: \alpha=(0 3 5 9)(1 13)(2 8 7 4)(6 12 10 11)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,5},{2,10,11},
      {5,7,10},{6,7,12}}
   C: \alpha=(0 3 2 12 6 8 7 11 10 4 5 9)(1 13)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,5},{2,10,11},
      {5,7,10},{6,7,12}}
 # of antimorphisms of SASC-graph: 52 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 16 
 |Aut(S)|=168 


 Subsystem No. 0 
 |Aut(T)|=24 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,11},{2,8,12},{2,9,13},{2,10,0},{3,7,0},{3,8,13},{3,9,12},{3,10,11},
 {4,7,10},{4,8,9},{4,11,0},{4,12,13},{5,7,13},{5,8,0},{5,9,11},{5,10,12},
 {6,7,12},{6,8,11},{6,9,0},{6,10,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 2)(3 5 4 6)(7 8 11 13 9 12 10)
      B_1={{2,3,6},{2,4,5},{2,7,11},{2,8,12},{2,9,13},{2,10,0},
      {5,7,13},{5,8,0},{5,9,11},{5,10,12},{6,7,12},{6,8,11},
      {6,9,0},{6,10,13}}
   B: \alpha=(0)(1 2)(3 5 4 6)(7 8)(9 11 10 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,0},{3,8,13},{3,9,12},{3,10,11},{4,7,10},{4,8,9},
      {4,11,0},{4,12,13}}
   C: \alpha=(0)(1 2)(3 5 4 6)(7 8 11 10 12 13 9)
      B_1={{2,3,6},{2,4,5},{2,7,11},{2,8,12},{2,9,13},{2,10,0},
      {5,7,13},{5,8,0},{5,9,11},{5,10,12},{6,7,12},{6,8,11},
      {6,9,0},{6,10,13}}
   D: \alpha=(0)(1 2)(3 5 4 6)(7 8)(9 12 10 11)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,0},{3,8,13},{3,9,12},{3,10,11},{4,7,10},{4,8,9},
      {4,11,0},{4,12,13}}
 # of antimorphisms of SASC-graph: 531 (fair: 105) 
 # of halving permutations: 72 (fair: 24; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=21 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,12},{2,9,13},{2,10,7},
 {3,8,13},{3,9,12},{3,10,11},{4,8,9},{4,11,7},{4,12,13},{5,8,7},{5,9,11},
 {5,10,12},{6,8,11},{6,9,7},{6,10,13}}
 I={{0,8},{1,9},{2,11},{3,7},{4,10},{5,13},{6,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 17 
 |Aut(S)|=24 


 Subsystem No. 0 
 |Aut(T)|=8 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,11},{2,8,12},{2,9,13},{2,10,0},{3,7,0},{3,8,13},{3,9,12},{3,10,11},
 {4,7,10},{4,8,11},{4,9,0},{4,12,13},{5,7,13},{5,8,9},{5,10,12},{5,11,0},
 {6,7,12},{6,8,0},{6,9,11},{6,10,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 7 9 13 8 10)(1 2 3)(4)(5 6)(11 12)
      B_1={{1,4,6},{1,8,10},{1,12,0},{2,3,6},{2,8,12},{2,9,13},
      {3,7,0},{3,9,12},{4,8,11},{4,9,0},{5,8,9},{5,11,0},
      {6,8,0},{6,9,11}}
   B: \alpha=(0 13)(1 2)(3)(4)(5 6)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,11,13},{2,7,11},{2,9,13},
      {3,7,0},{3,9,12},{4,7,10},{4,12,13},{5,7,13},{5,10,12},
      {6,7,12},{6,10,13}}
   E: \alpha=(0 10 8 12)(1 2)(3)(4)(5 6)(7 11 13 9)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,0},{3,8,13},{4,7,10},{4,12,13},{5,7,13},{5,8,9},
      {5,10,12},{5,11,0}}
 # of antimorphisms of SASC-graph: 17 (fair: 3) 
 # of halving permutations: 2 (fair: 2; strong: 2) 


 Subsystem No. 3 
 |Aut(T)|=24 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,11},{2,8,12},{2,9,13},{2,10,3},
 {4,7,10},{4,8,11},{4,9,3},{4,12,13},{5,7,13},{5,8,9},{5,10,12},{5,11,3},
 {6,7,12},{6,8,3},{6,9,11},{6,10,13}}
 I={{0,4},{1,5},{2,6},{7,3},{8,13},{9,12},{10,11}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 5)(2 6)(3 10 8 12)(4)(7 11 13 9)
      B_1={{0,1,2},{0,7,8},{0,13,3},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{4,7,10},{4,12,13},{6,7,12},{6,8,3},
      {6,9,11},{6,10,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 6) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=8 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,11},{2,8,12},{2,9,13},{2,10,4},
 {3,7,4},{3,8,13},{3,9,12},{3,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,4},
 {6,7,12},{6,8,4},{6,9,11},{6,10,13}}
 I={{0,3},{1,6},{2,5},{7,10},{8,11},{9,4},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 6)(2 5)(4 7 9 10 8 13 11 12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{2,3,6},
      {3,7,4},{3,8,13},{3,9,12},{3,10,11},{5,7,13},{5,8,9},
      {5,10,12},{5,11,4}}
   B: \alpha=(0)(1 6)(2 5)(3)(4 10 8 12)(7 11 13 9)
      B_1={{0,1,2},{0,7,8},{0,13,4},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,4},{3,7,4},{3,8,13},{5,7,13},{5,8,9},
      {5,10,12},{5,11,4}}
 # of antimorphisms of SASC-graph: 102 (fair: 38) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,12},{2,9,13},{2,10,7},
 {3,8,13},{3,9,12},{3,10,11},{4,8,11},{4,9,7},{4,12,13},{5,8,9},{5,10,12},
 {5,11,7},{6,8,7},{6,9,11},{6,10,13}}
 I={{0,8},{1,9},{2,11},{3,7},{4,10},{5,13},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 13 6 7)(2 11)(4 5 9 10 8 12)
      B_1={{0,11,12},{0,13,7},{1,3,5},{1,8,10},{1,11,13},{1,12,7},
      {3,10,11},{4,8,11},{4,9,7},{4,12,13},{5,8,9},{5,11,7},
      {6,9,11},{6,10,13}}
 # of antimorphisms of SASC-graph: 18 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 18 
 |Aut(S)|=4 


 Subsystem No. 0 
 |Aut(T)|=4 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,11},{2,8,12},{2,9,0},{2,10,13},{3,7,0},{3,8,9},{3,10,11},{3,12,13},
 {4,7,10},{4,8,13},{4,9,12},{4,11,0},{5,7,13},{5,8,0},{5,9,11},{5,10,12},
 {6,7,12},{6,8,11},{6,9,13},{6,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 2)(3 5 4 6)(7 8 11 10 12 13 9)
      B_1={{2,3,6},{2,4,5},{2,7,11},{2,8,12},{2,9,0},{2,10,13},
      {5,7,13},{5,8,0},{5,9,11},{5,10,12},{6,7,12},{6,8,11},
      {6,9,13},{6,10,0}}
   B: \alpha=(0)(1 2)(3 5 4 6)(7 8)(9 11 10 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,0},{3,8,9},{3,10,11},{3,12,13},{4,7,10},{4,8,13},
      {4,9,12},{4,11,0}}
   D: \alpha=(0 7 10 11)(1 5 2 6)(3 4)(8 9 12 13)
      B_1={{1,3,5},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},
      {2,7,11},{2,8,12},{2,9,0},{2,10,13},{3,7,0},{3,8,9},
      {3,10,11},{3,12,13}}
 # of antimorphisms of SASC-graph: 442 (fair: 106) 
 # of halving permutations: 2 (fair: 2; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,11},{2,8,12},{2,9,1},{2,10,13},{3,7,1},{3,8,9},{3,10,11},{3,12,13},
 {4,7,10},{4,8,13},{4,9,12},{4,11,1},{5,7,13},{5,8,1},{5,9,11},{5,10,12},
 {6,7,12},{6,8,11},{6,9,13},{6,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,2},{3,8,9},{3,10,11},{3,12,13},
 {4,7,10},{4,8,13},{4,9,12},{4,11,2},{5,7,13},{5,8,2},{5,9,11},{5,10,12},
 {6,7,12},{6,8,11},{6,9,13},{6,10,2}}
 I={{0,1},{3,6},{4,5},{7,11},{8,12},{9,2},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 5 2 7)(1 12 3 11)(4 9 8 6)(10 13)
      B_1={{0,3,4},{0,7,8},{0,11,12},{1,4,6},{1,8,10},{1,12,2},
      {3,8,9},{3,10,11},{4,7,10},{4,8,13},{4,11,2},{5,7,13},
      {5,8,2},{5,10,12}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,5},{2,7,11},{2,8,12},{2,9,3},{2,10,13},
 {4,7,10},{4,8,13},{4,9,12},{4,11,3},{5,7,13},{5,8,3},{5,9,11},{5,10,12},
 {6,7,12},{6,8,11},{6,9,13},{6,10,3}}
 I={{0,4},{1,5},{2,6},{7,3},{8,9},{10,11},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 6)(1 5)(3 7)(4)(8 9)(10 11)(12 13)
      B_1={{0,5,6},{0,9,10},{0,13,3},{2,4,5},{2,9,3},{2,10,13},
      {4,9,12},{4,11,3},{5,7,13},{5,8,3},{5,9,11},{5,10,12},
      {6,9,13},{6,10,3}}
   B: \alpha=(0)(1 5)(2 6)(3 7)(4)(8 9)(10 11)(12 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{2,7,11},{2,8,12},{4,7,10},{4,8,13},
      {6,7,12},{6,8,11}}
   E: \alpha=(0)(1 5)(2 6)(3 8 10 12)(4)(7 9 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{2,7,11},{2,8,12},{2,9,3},{2,10,13},
      {4,7,10},{4,11,3}}
 # of antimorphisms of SASC-graph: 33 (fair: 11) 
 # of halving permutations: 2 (fair: 2; strong: 2) 


 Subsystem No. 4 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,7,11},{2,8,12},{2,9,4},{2,10,13},
 {3,7,4},{3,8,9},{3,10,11},{3,12,13},{5,7,13},{5,8,4},{5,9,11},{5,10,12},
 {6,7,12},{6,8,11},{6,9,13},{6,10,4}}
 I={{0,3},{1,6},{2,5},{7,10},{8,13},{9,12},{11,4}}
 Examples of antimorphisms:
   A: \alpha=(0 4 5 7)(1 2 10 9)(3 11 12 6)(8 13)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},
      {1,8,10},{2,3,6},{2,8,12},{3,8,9},{3,12,13},{5,8,4},
      {5,9,11},{5,10,12}}
   B: \alpha=(0)(1 6)(2 5)(3)(4 8 10 12)(7 9 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,4},{2,7,11},{2,8,12},{2,9,4},{2,10,13},
      {3,7,4},{3,10,11}}
 # of antimorphisms of SASC-graph: 35 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,12},{2,9,7},{2,10,13},
 {3,8,9},{3,10,11},{3,12,13},{4,8,13},{4,9,12},{4,11,7},{5,8,7},{5,9,11},
 {5,10,12},{6,8,11},{6,9,13},{6,10,7}}
 I={{0,8},{1,9},{2,11},{3,7},{4,10},{5,13},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 11 7)(2 6 4 9)(3 8 12 10)(5 13)
      B_1={{0,1,2},{0,5,6},{1,3,5},{1,8,10},{1,12,7},{2,3,6},
      {2,4,5},{3,8,9},{4,9,12},{4,11,7},{5,8,7},{5,9,11},
      {5,10,12},{6,10,7}}
   B: \alpha=(0 4 8 10)(1 7 2 6)(3 11 12 9)(5 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,8,10},
      {1,12,7},{2,3,6},{2,4,5},{2,8,12},{3,8,9},{3,12,13},
      {5,8,7},{5,10,12}}
   C: \alpha=(0 2 4 7)(1 8 12 9 3 13)(5 11 10 6)
      B_1={{0,9,10},{0,13,7},{1,11,13},{2,4,5},{2,8,12},{2,9,7},
      {2,10,13},{3,8,9},{4,8,13},{5,8,7},{5,9,11},{6,8,11},
      {6,9,13},{6,10,7}}
 # of antimorphisms of SASC-graph: 52 (fair: 2) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,11},{2,9,8},{2,10,13},
 {3,7,8},{3,10,11},{3,12,13},{4,7,10},{4,9,12},{4,11,8},{5,7,13},{5,9,11},
 {5,10,12},{6,7,12},{6,9,13},{6,10,8}}
 I={{0,7},{1,10},{2,12},{3,9},{4,13},{5,8},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 4 8)(2 6 7 10)(3 9)(5 12 11 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{2,3,6},
      {2,4,5},{2,7,11},{3,7,8},{3,10,11},{3,12,13},{4,7,10},
      {4,11,8},{5,7,13}}
   B: \alpha=(0 1 7 10)(2 6 4 8)(3 9)(5 12 11 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{2,3,6},
      {2,4,5},{2,7,11},{3,7,8},{3,10,11},{3,12,13},{4,7,10},
      {4,11,8},{5,7,13}}
   C: \alpha=(0 1 11 12 7 10 5 13)(2 6 4 8)(3 9)
      B_1={{0,9,10},{0,13,8},{1,4,6},{1,7,9},{1,11,13},{1,12,8},
      {2,9,8},{2,10,13},{4,9,12},{5,9,11},{5,10,12},{6,7,12},
      {6,9,13},{6,10,8}}
 # of antimorphisms of SASC-graph: 56 (fair: 4) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 System No. 19 
 |Aut(S)|=12 


 Subsystem No. 0 
 |Aut(T)|=2 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,11},{2,8,13},{2,9,12},{2,10,0},{3,7,0},{3,8,11},{3,9,13},{3,10,12},
 {4,7,12},{4,8,9},{4,10,13},{4,11,0},{5,7,10},{5,8,0},{5,9,11},{5,12,13},
 {6,7,13},{6,8,12},{6,9,0},{6,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 4 7 11 3 9)(1 2)(5 8 13 6 10 12)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,0},{3,8,11},{3,10,12},{4,7,12},{5,8,0},{6,7,13},
      {6,8,12},{6,9,0}}
   B: \alpha=(0 4 12 5)(1 2)(3 11 6 13)(7 9 8 10)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,0},{3,8,11},{3,10,12},{4,7,12},{5,8,0},{6,7,13},
      {6,8,12},{6,9,0}}
   C: \alpha=(0 4 7 10 12 5 8 9)(1 2)(3 13 6 11)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,0},{3,8,11},{3,10,12},{4,7,12},{5,8,0},{6,7,13},
      {6,8,12},{6,9,0}}
 # of antimorphisms of SASC-graph: 14 (fair: 2) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=12 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,2},{3,8,11},{3,9,13},{3,10,12},
 {4,7,12},{4,8,9},{4,10,13},{4,11,2},{5,7,10},{5,8,2},{5,9,11},{5,12,13},
 {6,7,13},{6,8,12},{6,9,2},{6,10,11}}
 I={{0,1},{3,6},{4,5},{7,11},{8,13},{9,12},{10,2}}
 Examples of antimorphisms:
   B: \alpha=(0)(1)(2 10)(3 6)(4 5)(7 11)(8 13)(9 12)
      B_1={{0,3,4},{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,8,10},
      {3,7,2},{3,8,11},{3,9,13},{3,10,12},{4,7,12},{4,8,9},
      {4,10,13},{4,11,2}}
 # of antimorphisms of SASC-graph: 3 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,13},{2,9,12},{2,10,7},
 {3,8,11},{3,9,13},{3,10,12},{4,8,9},{4,10,13},{4,11,7},{5,8,7},{5,9,11},
 {5,12,13},{6,8,12},{6,9,7},{6,10,11}}
 I={{0,8},{1,9},{2,11},{3,7},{4,12},{5,10},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 7)(2 8 10 11 3 12)(4 9 13 5)
      B_1={{0,11,12},{0,13,7},{1,4,6},{1,8,10},{1,11,13},{1,12,7},
      {2,9,12},{3,8,11},{4,8,9},{4,11,7},{5,8,7},{5,9,11},
      {5,12,13},{6,8,12}}
 # of antimorphisms of SASC-graph: 18 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,5},{2,7,11},{2,8,13},{2,10,9},
 {3,7,9},{3,8,11},{3,10,12},{4,7,12},{4,10,13},{4,11,9},{5,7,10},{5,8,9},
 {5,12,13},{6,7,13},{6,8,12},{6,10,11}}
 I={{0,10},{1,7},{2,12},{3,13},{4,8},{5,11},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0 3 11 9)(1 6 10 2)(4 12 5 8 7 13)
      B_1={{0,3,4},{0,5,6},{1,3,5},{1,4,6},{2,3,6},{2,4,5},
      {2,7,11},{2,10,9},{3,7,9},{4,7,12},{4,11,9},{5,7,10},
      {5,8,9},{6,7,13}}
 # of antimorphisms of SASC-graph: 12 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 20 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,11},{2,8,13},{2,9,0},{2,10,12},{3,7,0},{3,8,9},{3,10,11},{3,12,13},
 {4,7,10},{4,8,12},{4,9,13},{4,11,0},{5,7,13},{5,8,11},{5,9,12},{5,10,0},
 {6,7,12},{6,8,0},{6,9,11},{6,10,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 2 8 4 10 5 1 7)(3 9 13 6)(11 12)
      B_1={{1,3,5},{1,11,13},{2,3,6},{2,4,5},{2,7,11},{2,8,13},
      {3,7,0},{3,10,11},{3,12,13},{4,7,10},{4,9,13},{4,11,0},
      {5,7,13},{5,8,11}}
   C: \alpha=(0 5 4 13 11 7)(1 12 6 8 10 2 3 9)
      B_1={{1,7,9},{1,8,10},{2,3,6},{2,7,11},{2,8,13},{2,9,0},
      {3,12,13},{4,8,12},{4,9,13},{5,7,13},{5,8,11},{5,9,12},
      {5,10,0},{6,7,12}}
 # of antimorphisms of SASC-graph: 10 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,11},{2,8,13},{2,9,1},{2,10,12},{3,7,1},{3,8,9},{3,10,11},{3,12,13},
 {4,7,10},{4,8,12},{4,9,13},{4,11,1},{5,7,13},{5,8,11},{5,9,12},{5,10,1},
 {6,7,12},{6,8,1},{6,9,11},{6,10,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 4 1 10)(2 7 5 8)(3 6 12 9)(11 13)
      B_1={{0,7,8},{0,9,10},{0,11,12},{2,8,13},{3,7,1},{3,8,9},
      {3,10,11},{4,7,10},{4,8,12},{4,11,1},{5,7,13},{6,7,12},
      {6,8,1},{6,9,11}}
 # of antimorphisms of SASC-graph: 16 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,5},{2,7,11},{2,8,13},{2,9,6},{2,10,12},
 {3,7,6},{3,8,9},{3,10,11},{3,12,13},{4,7,10},{4,8,12},{4,9,13},{4,11,6},
 {5,7,13},{5,8,11},{5,9,12},{5,10,6}}
 I={{0,5},{1,4},{2,3},{7,12},{8,6},{9,11},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 4)(2 3)(6 8 7 10 13 12)(9)(11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{2,4,5},
      {3,7,6},{3,8,9},{3,10,11},{3,12,13},{5,7,13},{5,8,11},
      {5,9,12},{5,10,6}}
   B: \alpha=(0 1 5 4)(2 3)(6 8)(7 12)(9)(10 13)(11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{2,4,5},
      {2,9,6},{3,7,6},{3,10,11},{3,12,13},{5,7,13},{5,8,11},
      {5,9,12},{5,10,6}}
   C: \alpha=(0 1 5 4)(2 3)(6 10 7 12 13 8)(9)(11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{2,4,5},
      {3,7,6},{3,8,9},{3,10,11},{3,12,13},{5,7,13},{5,8,11},
      {5,9,12},{5,10,6}}
   D: \alpha=(0 2 5 3)(1 4)(6 12 9 8 7 11)(10 13)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},
      {4,7,10},{4,8,12},{4,9,13},{4,11,6},{5,7,13},{5,8,11},
      {5,9,12},{5,10,6}}
 # of antimorphisms of SASC-graph: 108 (fair: 36) 
 # of halving permutations: 9 (fair: 3; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,4,5},{2,8,13},{2,9,7},{2,10,12},
 {3,8,9},{3,10,11},{3,12,13},{4,8,12},{4,9,13},{4,11,7},{5,8,11},{5,9,12},
 {5,10,7},{6,8,7},{6,9,11},{6,10,13}}
 I={{0,8},{1,9},{2,11},{3,7},{4,10},{5,13},{6,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,5},{2,7,11},{2,9,8},{2,10,12},
 {3,7,8},{3,10,11},{3,12,13},{4,7,10},{4,9,13},{4,11,8},{5,7,13},{5,9,12},
 {5,10,8},{6,7,12},{6,9,11},{6,10,13}}
 I={{0,7},{1,10},{2,13},{3,9},{4,12},{5,11},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,5},{2,7,11},{2,8,13},{2,10,12},
 {3,7,9},{3,10,11},{3,12,13},{4,7,10},{4,8,12},{4,11,9},{5,7,13},{5,8,11},
 {5,10,9},{6,7,12},{6,8,9},{6,10,13}}
 I={{0,10},{1,7},{2,9},{3,8},{4,13},{5,12},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 12 8)(2 5 3 13)(4 7 6 9 10 11)
      B_1={{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,11,13},{1,12,9},
      {2,7,11},{2,8,13},{3,7,9},{4,11,9},{5,7,13},{5,8,11},
      {5,10,9},{6,7,12}}
   B: \alpha=(0 10)(1 7)(2 4 11 12)(3)(5 9 13 6)(8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},
      {1,3,5},{1,4,6},{1,11,13},{1,12,9},{2,4,5},{3,12,13},
      {4,8,12},{6,8,9}}
   C: \alpha=(0 3 10)(1 7)(2 9)(4 11 12 13 6 5)(8)
      B_1={{0,1,2},{0,3,4},{0,11,12},{1,3,5},{1,8,10},{1,11,13},
      {2,3,6},{2,4,5},{2,7,11},{2,8,13},{2,10,12},{5,7,13},
      {5,8,11},{6,10,13}}
 # of antimorphisms of SASC-graph: 10 (fair: 2) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,5},{2,7,11},{2,8,13},{2,9,12},
 {3,7,12},{3,8,9},{3,10,11},{4,7,10},{4,9,13},{4,11,12},{5,7,13},{5,8,11},
 {5,10,12},{6,8,12},{6,9,11},{6,10,13}}
 I={{0,11},{1,12},{2,10},{3,13},{4,8},{5,9},{6,7}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 5 12 9)(2 10)(3 6 13 7)(4 8)(11)
      B_1={{0,1,2},{0,3,4},{0,13,12},{1,3,5},{1,4,6},{1,11,13},
      {2,4,5},{2,9,12},{3,7,12},{3,10,11},{4,7,10},{4,9,13},
      {4,11,12},{6,10,13}}
   D: \alpha=(0)(1 9 12 5)(2 10)(3 7 13 6)(4 8)(11)
      B_1={{0,1,2},{0,3,4},{0,13,12},{1,3,5},{1,4,6},{1,11,13},
      {2,4,5},{2,9,12},{3,7,12},{3,10,11},{4,7,10},{4,9,13},
      {4,11,12},{6,10,13}}
 # of antimorphisms of SASC-graph: 12 (fair: 12) 
 # of halving permutations: 2 (fair: 2; strong: 0) 


 System No. 21 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=3 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,12},{2,9,0},{2,11,13},{3,7,11},{3,8,13},{3,9,12},{3,10,0},
 {4,7,12},{4,8,0},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,0},
 {6,7,0},{6,8,10},{6,9,11},{6,12,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 2)(3 5 4 6)(7 8)(9 11 10 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,10,13},{2,7,10},{2,9,0},
      {3,7,11},{3,8,13},{3,9,12},{3,10,0},{4,7,12},{4,8,0},
      {4,9,13},{4,10,11}}
   D: \alpha=(0)(1 2)(3 5 4 6)(7 8)(9 12 10 11)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,10,13},{2,7,10},{2,9,0},
      {3,7,11},{3,8,13},{3,9,12},{3,10,0},{4,7,12},{4,8,0},
      {4,9,13},{4,10,11}}
 # of antimorphisms of SASC-graph: 24 (fair: 24) 
 # of halving permutations: 3 (fair: 3; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,12},{2,9,1},{2,11,13},{3,7,11},{3,8,13},{3,9,12},{3,10,1},
 {4,7,12},{4,8,1},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,1},
 {6,7,1},{6,8,10},{6,9,11},{6,12,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 2)(1 7 11 9 12)(3 6 5 4)(8 13 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {4,7,12},{4,8,1},{4,9,13},{4,10,11},{6,7,1},{6,8,10},
      {6,9,11},{6,12,13}}
   B: \alpha=(0 2)(1 12)(3 4 5 6)(7 9)(8)(10 13)(11)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {4,7,12},{4,8,1},{4,9,13},{4,10,11},{6,7,1},{6,8,10},
      {6,9,11},{6,12,13}}
   C: \alpha=(0 2)(1 7 11 9 12)(3 4 5 6)(8 13 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {4,7,12},{4,8,1},{4,9,13},{4,10,11},{6,7,1},{6,8,10},
      {6,9,11},{6,12,13}}
   D: \alpha=(0 4 2 6)(1 13 9 12 10 7)(3 5)(8)(11)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},
      {2,7,10},{2,8,12},{2,9,1},{2,11,13},{3,7,11},{3,8,13},
      {3,9,12},{3,10,1}}
 # of antimorphisms of SASC-graph: 70 (fair: 16) 
 # of halving permutations: 7 (fair: 1; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,7,11},{3,8,13},{3,9,12},{3,10,2},
 {4,7,12},{4,8,2},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,2},
 {6,7,2},{6,8,10},{6,9,11},{6,12,13}}
 I={{0,1},{3,6},{4,5},{7,10},{8,12},{9,2},{11,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 3 6)(4 8 13 5 12 11)(7 10)(9)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {3,7,11},{3,9,12},{4,7,12},{4,8,2},{4,9,13},{5,7,13},
      {6,7,2},{6,12,13}}
   B: \alpha=(0 1)(2 7 9 10)(3 6)(4)(5)(8 12)(11 13)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {4,8,2},{4,9,13},{5,8,9},{5,11,2},{6,7,2},{6,8,10},
      {6,9,11},{6,12,13}}
   C: \alpha=(0 3 1 6)(2)(4 5)(7 13 8 11 10 12)(9)
      B_1={{0,5,6},{1,3,5},{3,7,11},{3,8,13},{3,9,12},{3,10,2},
      {4,7,12},{4,8,2},{4,9,13},{4,10,11},{6,7,2},{6,8,10},
      {6,9,11},{6,12,13}}
   D: \alpha=(0 6 1 3)(2 9)(4 5)(7 10)(8)(11 13)(12)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,4,6},
      {1,7,9},{1,8,11},{1,10,13},{1,12,2},{4,7,12},{4,8,2},
      {4,9,13},{4,10,11}}
 # of antimorphisms of SASC-graph: 56 (fair: 14) 
 # of halving permutations: 5 (fair: 1; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,3,6},{2,4,5},{2,8,12},{2,9,7},{2,11,13},
 {3,8,13},{3,9,12},{3,10,7},{4,8,7},{4,9,13},{4,10,11},{5,8,9},{5,10,12},
 {5,11,7},{6,8,10},{6,9,11},{6,12,13}}
 I={{0,8},{1,9},{2,10},{3,11},{4,12},{5,13},{6,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,9,8},{2,11,13},
 {3,7,11},{3,9,12},{3,10,8},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,10,12},
 {5,11,8},{6,7,8},{6,9,11},{6,12,13}}
 I={{0,7},{1,11},{2,12},{3,13},{4,8},{5,9},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,6},{2,4,5},{2,7,10},{2,8,12},{2,11,13},
 {3,7,11},{3,8,13},{3,10,9},{4,7,12},{4,8,9},{4,10,11},{5,7,13},{5,10,12},
 {5,11,9},{6,7,9},{6,8,10},{6,12,13}}
 I={{0,10},{1,7},{2,9},{3,12},{4,13},{5,8},{6,11}}
 Examples of antimorphisms:
   B: \alpha=(0 2 10 9)(1 12 11 13)(3 6 4 7)(5)(8)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,11,12},{1,3,5},{1,4,6},
      {1,8,11},{1,10,13},{2,4,5},{3,7,11},{3,10,9},{4,10,11},
      {5,11,9},{6,8,10}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,6},{2,4,5},{2,8,12},{2,9,10},{2,11,13},
 {3,7,11},{3,8,13},{3,9,12},{4,7,12},{4,8,10},{4,9,13},{5,7,13},{5,8,9},
 {5,11,10},{6,7,10},{6,9,11},{6,12,13}}
 I={{0,9},{1,13},{2,7},{3,10},{4,11},{5,12},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 22 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,12},{2,9,0},{2,11,13},{3,7,11},{3,8,13},{3,9,12},{3,10,0},
 {4,7,0},{4,8,10},{4,9,11},{4,12,13},{5,7,12},{5,8,0},{5,9,13},{5,10,11},
 {6,7,13},{6,8,9},{6,10,12},{6,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 2)(3 5 4 6)(7 12 9 8 10 11)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},
      {5,7,12},{5,8,0},{5,9,13},{5,10,11},{6,7,13},{6,8,9},
      {6,10,12},{6,11,0}}
   B: \alpha=(0 13)(1)(2)(3 4)(5 6)(7 8)(9 12 10 11)
      B_1={{1,3,5},{1,7,9},{1,10,13},{2,3,6},{2,7,10},{2,9,0},
      {3,7,11},{3,8,13},{3,9,12},{3,10,0},{5,7,12},{5,8,0},
      {5,9,13},{5,10,11}}
   C: \alpha=(0)(1 2)(3 5 4 6)(7 11 10 8 9 12)(13)
      B_1={{2,3,6},{2,4,5},{2,7,10},{2,8,12},{2,9,0},{2,11,13},
      {3,7,11},{3,8,13},{3,9,12},{3,10,0},{4,7,0},{4,8,10},
      {4,9,11},{4,12,13}}
   D: \alpha=(0 13)(1)(2)(3 4)(5 6)(7 8)(9 11 10 12)
      B_1={{1,3,5},{1,7,9},{1,10,13},{2,3,6},{2,7,10},{2,9,0},
      {3,7,11},{3,8,13},{3,9,12},{3,10,0},{5,7,12},{5,8,0},
      {5,9,13},{5,10,11}}
 # of antimorphisms of SASC-graph: 28 (fair: 4) 
 # of halving permutations: 10 (fair: 2; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,5},
 {2,7,10},{2,8,12},{2,9,1},{2,11,13},{3,7,11},{3,8,13},{3,9,12},{3,10,1},
 {4,7,1},{4,8,10},{4,9,11},{4,12,13},{5,7,12},{5,8,1},{5,9,13},{5,10,11},
 {6,7,13},{6,8,9},{6,10,12},{6,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 2)(1)(3 4 5 6)(7 8 9 13 11 10)(12)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {3,7,11},{3,8,13},{3,9,12},{3,10,1},{5,7,12},{5,8,1},
      {5,9,13},{5,10,11}}
   B: \alpha=(0 2)(1 12)(3 4 5 6)(7 9)(8)(10 13)(11)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {3,7,11},{3,8,13},{3,9,12},{3,10,1},{5,7,12},{5,8,1},
      {5,9,13},{5,10,11}}
   C: \alpha=(0 3 2 5)(1 7 13 11 10 9 12)(4 6)(8)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,4,5},
      {2,7,10},{2,8,12},{2,9,1},{2,11,13},{4,7,1},{4,8,10},
      {4,9,11},{4,12,13}}
   D: \alpha=(0 4 2 6)(1 7 10 12 9 13)(3 5)(8)(11)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},
      {2,7,10},{2,8,12},{2,9,1},{2,11,13},{3,7,11},{3,8,13},
      {3,9,12},{3,10,1}}
 # of antimorphisms of SASC-graph: 64 (fair: 16) 
 # of halving permutations: 7 (fair: 1; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,6},{2,7,10},{2,8,12},{2,9,5},{2,11,13},
 {3,7,11},{3,8,13},{3,9,12},{3,10,5},{4,7,5},{4,8,10},{4,9,11},{4,12,13},
 {6,7,13},{6,8,9},{6,10,12},{6,11,5}}
 I={{0,6},{1,3},{2,4},{7,12},{8,5},{9,13},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 3)(2 4)(5 9 10 11 13)(7 12 8)
      B_1={{0,3,4},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,5},
      {2,7,10},{2,8,12},{2,9,5},{2,11,13},{3,7,11},{3,8,13},
      {3,9,12},{3,10,5}}
   B: \alpha=(0 1 6 3)(2 4)(5)(7 12)(8)(9 13)(10 11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{2,3,6},
      {4,7,5},{4,8,10},{4,9,11},{4,12,13},{6,7,13},{6,8,9},
      {6,10,12},{6,11,5}}
 # of antimorphisms of SASC-graph: 48 (fair: 6) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,3,6},{2,4,5},{2,8,12},{2,9,7},{2,11,13},
 {3,8,13},{3,9,12},{3,10,7},{4,8,10},{4,9,11},{4,12,13},{5,8,7},{5,9,13},
 {5,10,11},{6,8,9},{6,10,12},{6,11,7}}
 I={{0,8},{1,9},{2,10},{3,11},{4,7},{5,12},{6,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,6},{2,4,5},{2,7,10},{2,9,8},{2,11,13},
 {3,7,11},{3,9,12},{3,10,8},{4,7,8},{4,9,11},{4,12,13},{5,7,12},{5,9,13},
 {5,10,11},{6,7,13},{6,10,12},{6,11,8}}
 I={{0,7},{1,11},{2,12},{3,13},{4,10},{5,8},{6,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,6},{2,4,5},{2,7,10},{2,8,12},{2,11,13},
 {3,7,11},{3,8,13},{3,10,9},{4,7,9},{4,8,10},{4,12,13},{5,7,12},{5,8,9},
 {5,10,11},{6,7,13},{6,10,12},{6,11,9}}
 I={{0,10},{1,7},{2,9},{3,12},{4,11},{5,13},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,6},{2,4,5},{2,7,10},{2,8,12},{2,11,13},
 {3,7,11},{3,8,13},{3,9,12},{4,8,10},{4,9,11},{4,12,13},{5,7,12},{5,9,13},
 {5,10,11},{6,7,13},{6,8,9},{6,10,12}}
 I={{0,13},{1,12},{2,9},{3,10},{4,7},{5,8},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 23 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,13},{3,9,11},{3,10,0},
 {4,5,13},{4,8,9},{4,10,12},{4,11,0},{5,7,11},{5,8,0},{5,9,12},{6,7,0},
 {6,8,12},{6,9,13},{6,10,11},{7,10,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,13},{3,9,11},{3,10,1},
 {4,5,13},{4,8,9},{4,10,12},{4,11,1},{5,7,11},{5,8,1},{5,9,12},{6,7,1},
 {6,8,12},{6,9,13},{6,10,11},{7,10,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,13},{3,9,11},{3,10,2},
 {4,5,13},{4,8,9},{4,10,12},{4,11,2},{5,7,11},{5,8,2},{5,9,12},{6,7,2},
 {6,8,12},{6,9,13},{6,10,11},{7,10,13}}
 I={{0,1},{3,6},{4,7},{5,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   C: \alpha=(0 1)(2 4 13 6)(3 11 5 12)(7 8 10 9)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,2},
      {3,8,13},{3,9,11},{4,8,9},{4,11,2},{5,8,2},{5,9,12},
      {6,8,12},{6,9,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,10},{2,8,11},{2,9,3},{2,12,13},
 {4,5,13},{4,8,9},{4,10,12},{4,11,3},{5,7,11},{5,8,3},{5,9,12},{6,7,3},
 {6,8,12},{6,9,13},{6,10,11},{7,10,13}}
 I={{0,4},{1,5},{2,6},{7,12},{8,13},{9,11},{10,3}}
 Examples of antimorphisms:
   A: \alpha=(0 4)(1)(2 6)(3 10)(5 7 12)(8 13)(9 11)
      B_1={{1,4,6},{1,7,9},{1,8,10},{2,4,7},{2,5,10},{2,12,13},
      {4,5,13},{4,8,9},{4,10,12},{4,11,3},{5,9,12},{6,9,13},
      {6,10,11},{7,10,13}}
   B: \alpha=(0 4)(1)(2 6)(3 10)(5)(7 12)(8 13)(9 11)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},
      {1,11,13},{1,12,3},{2,8,11},{2,9,3},{5,7,11},{5,8,3},
      {6,7,3},{6,8,12}}
 # of antimorphisms of SASC-graph: 9 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,10},{2,8,11},{2,9,4},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,4},{5,7,11},{5,8,4},{5,9,12},{6,7,4},
 {6,8,12},{6,9,13},{6,10,11},{7,10,13}}
 I={{0,3},{1,6},{2,7},{5,13},{8,9},{10,12},{11,4}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,11},{2,9,5},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,5},{4,8,9},{4,10,12},{4,11,5},{6,7,5},
 {6,8,12},{6,9,13},{6,10,11},{7,10,13}}
 I={{0,6},{1,3},{2,10},{4,13},{7,11},{8,5},{9,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 13)(2 11 4 9)(3 12 10 6)(5 8)
      B_1={{0,9,10},{0,11,12},{0,13,5},{1,7,9},{1,11,13},{1,12,5},
      {2,9,5},{3,7,12},{3,9,11},{4,11,5},{6,7,5},{6,8,12},
      {6,9,13},{6,10,11}}
 # of antimorphisms of SASC-graph: 16 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,10},{2,8,11},{2,9,6},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,6},{4,5,13},{4,8,9},{4,10,12},{4,11,6},
 {5,7,11},{5,8,6},{5,9,12},{7,10,13}}
 I={{0,5},{1,4},{2,3},{7,6},{8,12},{9,13},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 3 1 6 10 8 4 5 12 11 2 7)(9 13)
      B_1={{0,7,8},{0,9,10},{1,3,5},{1,7,9},{2,8,11},{2,9,6},
      {3,7,12},{3,9,11},{3,10,6},{4,8,9},{4,11,6},{5,7,11},
      {5,8,6},{5,9,12}}
   B: \alpha=(0 3 10 8)(1 7 4 6)(2 11 12 5)(9 13)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{0,13,6},{1,8,10},
      {1,11,13},{1,12,6},{2,4,7},{2,5,10},{2,12,13},{4,5,13},
      {4,10,12},{7,10,13}}
 # of antimorphisms of SASC-graph: 40 (fair: 8) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,10},{2,8,11},{2,9,7},{2,12,13},
 {3,8,13},{3,9,11},{3,10,7},{4,5,13},{4,8,9},{4,10,12},{4,11,7},{5,8,7},
 {5,9,12},{6,8,12},{6,9,13},{6,10,11}}
 I={{0,8},{1,9},{2,4},{3,12},{5,11},{6,7},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 4 5 9)(1 8 13 12)(2 11 10 3)(6 7)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},
      {1,11,13},{1,12,7},{2,3,6},{2,5,10},{3,8,13},{4,5,13},
      {5,8,7},{6,10,11}}
   B: \alpha=(0 7 4 1)(2 9 8 6)(3 12)(5 13 11 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{1,3,5},{1,11,13},{2,3,6},
      {2,5,10},{2,8,11},{3,8,13},{3,9,11},{3,10,7},{4,8,9},
      {4,11,7},{5,8,7}}
   C: \alpha=(0 5 11 8 10 13)(1 3 9 4 12 2)(6 7)
      B_1={{0,1,2},{0,3,4},{0,13,7},{1,12,7},{2,5,10},{2,8,11},
      {2,9,7},{3,8,13},{3,9,11},{3,10,7},{4,5,13},{4,10,12},
      {4,11,7},{5,8,7}}
   D: \alpha=(0 1 4 7)(2 6 8 9)(3 12)(5 10 11 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{1,3,5},{1,11,13},{2,3,6},
      {2,5,10},{2,8,11},{3,8,13},{3,9,11},{3,10,7},{4,8,9},
      {4,11,7},{5,8,7}}
 # of antimorphisms of SASC-graph: 10 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,10},{2,9,8},{2,12,13},
 {3,7,12},{3,9,11},{3,10,8},{4,5,13},{4,10,12},{4,11,8},{5,7,11},{5,9,12},
 {6,7,8},{6,9,13},{6,10,11},{7,10,13}}
 I={{0,7},{1,10},{2,11},{3,13},{4,9},{5,8},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 2 5 12)(1 4 7 11)(3 13)(6 10 9 8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{2,3,6},{3,7,12},{3,9,11},{3,10,8},{5,7,11},
      {5,9,12},{6,7,8}}
   B: \alpha=(0 2 7 11)(1 4 5 12)(3 13)(6 10 9 8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,13,8},{1,3,5},
      {1,4,6},{1,7,9},{3,7,12},{3,10,8},{5,7,11},{5,9,12},
      {6,7,8},{7,10,13}}
 # of antimorphisms of SASC-graph: 40 (fair: 4) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,12,13},
 {3,7,12},{3,8,13},{3,10,9},{4,5,13},{4,10,12},{4,11,9},{5,7,11},{5,8,9},
 {6,7,9},{6,8,12},{6,10,11},{7,10,13}}
 I={{0,10},{1,7},{2,9},{3,11},{4,8},{5,12},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 12 7 8 10 4 2 11 5 9 3)(6 13)
      B_1={{0,1,2},{0,5,6},{1,3,5},{1,4,6},{1,8,10},{2,3,6},
      {2,4,7},{2,5,10},{3,7,12},{3,10,9},{5,7,11},{6,7,9},
      {6,8,12},{6,10,11}}
   C: \alpha=(0 3 10 11 2 1 5 13)(4 9 6 8 7 12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,4,6},{2,3,6},
      {2,4,7},{2,5,10},{4,5,13},{4,10,12},{5,7,11},{6,7,9},
      {6,10,11},{7,10,13}}
 # of antimorphisms of SASC-graph: 10 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,8,11},{2,9,10},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{4,5,13},{4,8,9},{4,11,10},{5,7,11},{5,8,10},
 {5,9,12},{6,7,10},{6,8,12},{6,9,13}}
 I={{0,9},{1,8},{2,5},{3,10},{4,12},{6,11},{7,13}}
 Examples of antimorphisms:
   A: \alpha=(0 9)(1 2 6 4 8 5 13 3)(7 12 11 10)
      B_1={{1,3,5},{1,7,9},{2,3,6},{2,4,7},{2,8,11},{2,9,10},
      {3,7,12},{3,9,11},{4,5,13},{4,8,9},{4,11,10},{5,7,11},
      {5,9,12},{6,9,13}}
   B: \alpha=(0 9)(1 2 8 5)(3 13 4 6)(7 12 11 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},
      {1,4,6},{1,11,13},{1,12,10},{2,12,13},{3,8,13},{5,8,10},
      {6,7,10},{6,8,12}}
   C: \alpha=(0 9)(1 5 8 2 12 7 10 11)(3 6 4 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},
      {1,4,6},{1,11,13},{1,12,10},{2,12,13},{3,8,13},{5,8,10},
      {6,7,10},{6,8,12}}
 # of antimorphisms of SASC-graph: 30 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,5,10},{2,9,11},{2,12,13},
 {3,7,12},{3,8,13},{3,10,11},{4,5,13},{4,8,9},{4,10,12},{5,8,11},{5,9,12},
 {6,7,11},{6,8,12},{6,9,13},{7,10,13}}
 I={{0,12},{1,13},{2,8},{3,9},{4,11},{5,7},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 5 13 9 11 12 7 10)(1 3 8 4 6 2)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,13,11},{1,4,6},{1,7,9},
      {1,8,10},{1,12,11},{3,8,13},{5,8,11},{6,7,11},{6,8,12},
      {6,9,13},{7,10,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,9,12},
 {3,8,13},{3,9,11},{3,10,12},{4,5,13},{4,8,9},{4,11,12},{5,7,11},{5,8,12},
 {6,7,12},{6,9,13},{6,10,11},{7,10,13}}
 I={{0,11},{1,12},{2,13},{3,7},{4,10},{5,9},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 3 12 9)(1 2 6 7)(4 10)(5 11 13 8)
      B_1={{0,1,2},{0,3,4},{0,7,8},{1,4,6},{1,8,10},{2,8,11},
      {2,9,12},{3,8,13},{3,9,11},{4,8,9},{4,11,12},{5,7,11},
      {6,7,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 12 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,9,13},
 {3,7,12},{3,9,11},{3,10,13},{4,8,9},{4,10,12},{4,11,13},{5,7,11},{5,8,13},
 {5,9,12},{6,7,13},{6,8,12},{6,10,11}}
 I={{0,13},{1,11},{2,12},{3,8},{4,5},{6,9},{7,10}}
 Examples of antimorphisms:
   A: \alpha=(0 7 13 10)(1 3 9 4 6 5 11 8)(2 12)
      B_1={{0,9,10},{0,11,12},{1,4,6},{1,7,9},{1,8,10},{1,12,13},
      {3,7,12},{3,9,11},{4,10,12},{5,7,11},{5,9,12},{6,7,13},
      {6,8,12},{6,10,11}}
   B: \alpha=(0 4 11 7)(1 10 13 5)(2)(3 8)(6 9)(12)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,3,5},{1,4,6},{1,7,9},
      {1,12,13},{2,8,11},{2,9,13},{3,10,13},{4,8,9},{4,11,13},
      {6,7,13},{6,8,12}}
   D: \alpha=(0 4 11 7)(1 10 13 5)(2 12)(3 8)(6)(9)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,11,12},{1,3,5},{1,7,9},
      {1,12,13},{2,3,6},{2,8,11},{2,9,13},{3,10,13},{4,8,9},
      {4,11,13},{6,10,11}}
 # of antimorphisms of SASC-graph: 49 (fair: 21) 
 # of halving permutations: 3 (fair: 3; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{4,5,13},{4,8,9},{4,10,12},{5,7,11},{5,9,12},
 {6,8,12},{6,9,13},{6,10,11},{7,10,13}}
 I={{0,13},{1,12},{2,9},{3,10},{4,11},{5,8},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 2 11 13 12 7)(1 4 5 9 6 8)(3 10)
      B_1={{0,7,8},{0,9,10},{1,7,9},{1,8,10},{2,4,7},{2,5,10},
      {2,8,11},{2,12,13},{4,5,13},{4,8,9},{4,10,12},{6,9,13},
      {6,10,11},{7,10,13}}
   B: \alpha=(0 4 5 7)(1 2 12 9)(3 10)(6 13 11 8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,11,13},{2,3,6},{3,7,12},{3,8,13},{3,9,11},{5,7,11},
      {5,9,12},{6,8,12}}
   C: \alpha=(0 4 12 8 11 9)(1 13 6 2 5 7)(3 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,11,13},{2,3,6},{3,7,12},{3,8,13},{3,9,11},{5,7,11},
      {5,9,12},{6,8,12}}
 # of antimorphisms of SASC-graph: 42 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 24 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,13},{3,9,11},{3,10,0},
 {4,5,11},{4,8,0},{4,9,12},{4,10,13},{5,7,0},{5,8,12},{5,9,13},{6,7,13},
 {6,8,9},{6,10,12},{6,11,0},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 3 11 5 13 4 12 6)(1)(2)(7 8)(9 10)
      B_1={{1,3,5},{1,4,6},{1,7,9},{2,3,6},{2,4,7},{2,5,10},
      {3,7,12},{3,10,0},{4,5,11},{4,10,13},{5,7,0},{6,7,13},
      {6,10,12},{7,10,11}}
   D: \alpha=(0 4 11 6 13 3 12 5)(1)(2)(7 8)(9 10)
      B_1={{1,3,5},{1,4,6},{1,7,9},{2,3,6},{2,4,7},{2,5,10},
      {3,7,12},{3,10,0},{4,5,11},{4,10,13},{5,7,0},{6,7,13},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 8 (fair: 8) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,13},{3,9,11},{3,10,1},
 {4,5,11},{4,8,1},{4,9,12},{4,10,13},{5,7,1},{5,8,12},{5,9,13},{6,7,13},
 {6,8,9},{6,10,12},{6,11,1},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 3 11 5 13 4 12 6)(2)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,7},{2,5,10},
      {3,7,12},{3,10,1},{4,5,11},{4,10,13},{5,7,1},{6,7,13},
      {6,10,12},{7,10,11}}
   B: \alpha=(0)(1 4 13 3)(2)(5 12 6 11)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,7},{2,5,10},
      {3,7,12},{3,8,13},{3,9,11},{4,5,11},{4,8,1},{4,9,12},
      {6,10,12},{7,10,11}}
   D: \alpha=(0)(1 3 13 4)(2)(5 11 6 12)(7 9)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{2,3,6},{2,4,7},{2,5,10},
      {3,7,12},{3,8,13},{3,9,11},{4,5,11},{4,8,1},{4,9,12},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 17 (fair: 7) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,13},{3,9,11},{3,10,2},
 {4,5,11},{4,8,2},{4,9,12},{4,10,13},{5,7,2},{5,8,12},{5,9,13},{6,7,13},
 {6,8,9},{6,10,12},{6,11,2},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 3 13 4)(5 11 6 12)(7 9 10 8)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{1,3,5},{1,4,6},
      {3,7,12},{3,10,2},{4,5,11},{4,10,13},{5,7,2},{6,7,13},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,10},{2,8,11},{2,9,3},{2,12,13},
 {4,5,11},{4,8,3},{4,9,12},{4,10,13},{5,7,3},{5,8,12},{5,9,13},{6,7,13},
 {6,8,9},{6,10,12},{6,11,3},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,12},{8,13},{9,11},{10,3}}
 Examples of antimorphisms:
   A: \alpha=(0 2 5 3)(1 10 7 13)(4 6 12 8)(9 11)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,4,6},
      {1,7,9},{1,8,10},{4,5,11},{4,9,12},{5,7,3},{5,8,12},
      {5,9,13},{6,7,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,10},{2,8,11},{2,9,4},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,4},{5,7,4},{5,8,12},{5,9,13},{6,7,13},
 {6,8,9},{6,10,12},{6,11,4},{7,10,11}}
 I={{0,3},{1,6},{2,7},{5,11},{8,4},{9,12},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 13 11)(1 12 7 6 4 3)(5 9 8 10)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,13,4},{1,7,9},{1,8,10},
      {1,11,13},{1,12,4},{2,9,4},{3,10,4},{5,7,4},{5,9,13},
      {6,7,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,11},{2,9,5},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,5},{4,8,5},{4,9,12},{4,10,13},{6,7,13},
 {6,8,9},{6,10,12},{6,11,5},{7,10,11}}
 I={{0,6},{1,3},{2,10},{4,11},{7,5},{8,12},{9,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 3 8)(1 11 5 10)(4 7 12 6)(9 13)
      B_1={{0,7,8},{0,9,10},{1,7,9},{1,8,10},{2,3,6},{2,4,7},
      {2,8,11},{2,9,5},{3,9,11},{6,7,13},{6,8,9},{6,10,12},
      {6,11,5},{7,10,11}}
   B: \alpha=(0 3 9 12)(1 13 8 6)(2 10)(4 11)(5)(7)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,13,5},{1,7,9},
      {1,8,10},{1,11,13},{2,4,7},{2,8,11},{2,9,5},{4,9,12},
      {6,8,9},{6,11,5}}
   C: \alpha=(0 3 8 6 1 12)(2 10)(4 5 11)(7)(9 13)
      B_1={{0,11,12},{0,13,5},{1,4,6},{1,11,13},{2,3,6},{2,12,13},
      {3,7,12},{3,8,13},{3,10,5},{4,8,5},{4,10,13},{6,7,13},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 50 (fair: 6) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,10},{2,8,11},{2,9,6},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{3,10,6},{4,5,11},{4,8,6},{4,9,12},{4,10,13},
 {5,7,6},{5,8,12},{5,9,13},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,13},{8,9},{10,12},{11,6}}
 Examples of antimorphisms:
   A: \alpha=(0 5)(1 4)(2 6 11)(3)(7 13)(8 9)(10 12)
      B_1={{1,3,5},{2,4,7},{2,5,10},{2,8,11},{3,8,13},{3,10,6},
      {4,5,11},{4,8,6},{4,9,12},{4,10,13},{5,7,6},{5,8,12},
      {5,9,13},{7,10,11}}
   B: \alpha=(0 5)(1 4)(2)(3)(6 11)(7 13)(8 9)(10 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},
      {1,7,9},{1,8,10},{1,11,13},{1,12,6},{2,8,11},{2,12,13},
      {3,7,12},{3,9,11}}
 # of antimorphisms of SASC-graph: 9 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,10},{2,8,11},{2,9,7},{2,12,13},
 {3,8,13},{3,9,11},{3,10,7},{4,5,11},{4,8,7},{4,9,12},{4,10,13},{5,8,12},
 {5,9,13},{6,8,9},{6,10,12},{6,11,7}}
 I={{0,8},{1,9},{2,4},{3,12},{5,7},{6,13},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 2 7 3)(1 11 8 4)(5 12 9 10)(6 13)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,7},{1,8,10},{1,11,13},
      {1,12,7},{2,12,13},{3,8,13},{3,10,7},{4,8,7},{4,10,13},
      {5,8,12},{5,9,13}}
   B: \alpha=(0 4 8 2)(1 3 7 11)(5 10 9 12)(6 13)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,8,10},
      {1,11,13},{1,12,7},{3,8,13},{3,10,7},{4,8,7},{5,8,12},
      {5,9,13},{6,8,9}}
   D: \alpha=(0 2 8 4)(1 11 7 3)(5 12 9 10)(6 13)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,8,10},
      {1,11,13},{1,12,7},{3,8,13},{3,10,7},{4,8,7},{5,8,12},
      {5,9,13},{6,8,9}}
 # of antimorphisms of SASC-graph: 38 (fair: 2) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,10},{2,9,8},{2,12,13},
 {3,7,12},{3,9,11},{3,10,8},{4,5,11},{4,9,12},{4,10,13},{5,7,8},{5,9,13},
 {6,7,13},{6,10,12},{6,11,8},{7,10,11}}
 I={{0,7},{1,10},{2,11},{3,13},{4,8},{5,12},{6,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,12,13},
 {3,7,12},{3,8,13},{3,10,9},{4,5,11},{4,8,9},{4,10,13},{5,7,9},{5,8,12},
 {6,7,13},{6,10,12},{6,11,9},{7,10,11}}
 I={{0,10},{1,7},{2,9},{3,11},{4,12},{5,13},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 6 7 9)(1 2 11 4)(3 12 10 8)(5 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{1,3,5},
      {1,8,10},{2,4,7},{2,5,10},{3,7,12},{4,5,11},{5,7,9},
      {5,8,12},{7,10,11}}
   C: \alpha=(0 6 7 9)(1 2 3 12)(4 10 8 11)(5 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{1,3,5},
      {1,8,10},{2,4,7},{2,5,10},{3,7,12},{4,5,11},{5,7,9},
      {5,8,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 14 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,8,11},{2,9,10},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{4,5,11},{4,8,10},{4,9,12},{5,7,10},{5,8,12},
 {5,9,13},{6,7,13},{6,8,9},{6,11,10}}
 I={{0,9},{1,8},{2,5},{3,10},{4,13},{6,12},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,5,10},{2,9,11},{2,12,13},
 {3,7,12},{3,8,13},{3,10,11},{4,8,11},{4,9,12},{4,10,13},{5,7,11},{5,8,12},
 {5,9,13},{6,7,13},{6,8,9},{6,10,12}}
 I={{0,12},{1,13},{2,8},{3,9},{4,5},{6,11},{7,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 8)(2 12 11 10)(4 9 6 5 13 7)
      B_1={{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,8,10},{1,12,11},
      {2,4,7},{2,5,10},{2,9,11},{3,7,12},{5,7,11},{5,8,12},
      {5,9,13},{6,8,9}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,9,12},
 {3,8,13},{3,9,11},{3,10,12},{4,5,11},{4,8,12},{4,10,13},{5,7,12},{5,9,13},
 {6,7,13},{6,8,9},{6,11,12},{7,10,11}}
 I={{0,11},{1,12},{2,13},{3,7},{4,9},{5,8},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 8 6)(2 10 11 4)(3 9 5 7 13 12)
      B_1={{0,3,4},{0,5,6},{1,3,5},{1,4,6},{1,8,10},{1,11,13},
      {2,3,6},{2,5,10},{3,8,13},{3,10,12},{4,5,11},{4,10,13},
      {5,9,13},{6,7,13}}
   B: \alpha=(0 3 11 7)(1 13 6 5)(2 10 8 12)(4 9)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{1,4,6},{1,7,9},
      {1,8,10},{1,11,13},{2,3,6},{2,8,11},{2,9,12},{3,9,11},
      {6,8,9},{6,11,12}}
   D: \alpha=(0 7 11 3)(1 5 6 13)(2 12 8 10)(4 9)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{1,4,6},{1,7,9},
      {1,8,10},{1,11,13},{2,3,6},{2,8,11},{2,9,12},{3,9,11},
      {6,8,9},{6,11,12}}
 # of antimorphisms of SASC-graph: 46 (fair: 4) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,9,13},
 {3,7,12},{3,9,11},{3,10,13},{4,5,11},{4,8,13},{4,9,12},{5,7,13},{5,8,12},
 {6,8,9},{6,10,12},{6,11,13},{7,10,11}}
 I={{0,13},{1,11},{2,12},{3,8},{4,10},{5,9},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 6 12 9)(2 5 11 7)(3 8 13)(4 10)
      B_1={{0,1,2},{0,3,4},{0,11,12},{1,4,6},{2,3,6},{2,4,7},
      {2,8,11},{2,9,13},{3,9,11},{4,5,11},{4,8,13},{4,9,12},
      {6,8,9},{6,11,13}}
   B: \alpha=(0)(1 6 12 9)(2 5 11 7)(3 8)(4 10)(13)
      B_1={{0,1,2},{0,3,4},{0,11,12},{1,3,5},{1,4,6},{1,12,13},
      {2,3,6},{2,4,7},{3,7,12},{3,9,11},{3,10,13},{4,5,11},
      {4,9,12},{5,7,13}}
 # of antimorphisms of SASC-graph: 11 (fair: 5) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,12,13},
 {3,7,12},{3,8,13},{3,9,11},{4,5,11},{4,9,12},{4,10,13},{5,8,12},{5,9,13},
 {6,7,13},{6,8,9},{6,10,12},{7,10,11}}
 I={{0,13},{1,12},{2,9},{3,10},{4,8},{5,7},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 8)(2 10 11 4)(3 13 12 9)(5 7)
      B_1={{0,1,2},{0,5,6},{0,11,12},{1,3,5},{1,11,13},{2,3,6},
      {2,4,7},{2,8,11},{2,12,13},{3,7,12},{3,9,11},{5,8,12},
      {6,8,9},{7,10,11}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 25 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,10},{2,8,11},{2,9,0},{2,12,13},{3,7,12},{3,8,0},{3,9,13},{3,10,11},
 {4,5,0},{4,8,12},{4,9,11},{4,10,13},{5,7,11},{5,8,13},{5,9,12},{6,7,13},
 {6,8,9},{6,10,12},{6,11,0},{7,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 2 12 5)(1 4 8 13)(3 7 11 6)(9 10)
      B_1={{1,3,5},{1,11,13},{1,12,0},{2,3,6},{2,8,11},{2,9,0},
      {3,8,0},{3,9,13},{3,10,11},{4,8,12},{4,9,11},{4,10,13},
      {5,7,11},{5,9,12}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,10},{2,8,11},{2,9,1},{2,12,13},{3,7,12},{3,8,1},{3,9,13},{3,10,11},
 {4,5,1},{4,8,12},{4,9,11},{4,10,13},{5,7,11},{5,8,13},{5,9,12},{6,7,13},
 {6,8,9},{6,10,12},{6,11,1},{7,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 4 9 10 6 13)(1 3 7 2 8 12 5 11)
      B_1={{0,11,12},{0,13,1},{2,3,6},{2,4,7},{2,5,10},{2,12,13},
      {3,8,1},{3,9,13},{3,10,11},{4,8,12},{4,9,11},{4,10,13},
      {5,7,11},{6,10,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,2},{3,9,13},{3,10,11},
 {4,5,2},{4,8,12},{4,9,11},{4,10,13},{5,7,11},{5,8,13},{5,9,12},{6,7,13},
 {6,8,9},{6,10,12},{6,11,2},{7,10,2}}
 I={{0,1},{3,6},{4,7},{5,10},{8,11},{9,2},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 3 11 7)(1 6 2 10)(4 9 5 8)(12 13)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,2},{1,7,9},{1,8,10},
      {1,11,13},{1,12,2},{3,8,2},{4,8,12},{5,7,11},{5,9,12},
      {6,8,9},{6,11,2}}
   C: \alpha=(0 1)(2 4 11 5 12 3 13 6)(7 8 10 9)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {3,8,2},{3,9,13},{4,8,12},{4,9,11},{5,8,13},{5,9,12},
      {6,8,9},{6,11,2}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,10},{2,8,11},{2,9,3},{2,12,13},
 {4,5,3},{4,8,12},{4,9,11},{4,10,13},{5,7,11},{5,8,13},{5,9,12},{6,7,13},
 {6,8,9},{6,10,12},{6,11,3},{7,10,3}}
 I={{0,4},{1,5},{2,6},{7,12},{8,3},{9,13},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,10},{2,8,11},{2,9,4},{2,12,13},
 {3,7,12},{3,8,4},{3,9,13},{3,10,11},{5,7,11},{5,8,13},{5,9,12},{6,7,13},
 {6,8,9},{6,10,12},{6,11,4},{7,10,4}}
 I={{0,3},{1,6},{2,7},{5,4},{8,12},{9,11},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 5 2 13 11 7 10 12)(1 8 4 6 3 9)
      B_1={{0,11,12},{0,13,4},{1,3,5},{1,7,9},{1,11,13},{1,12,4},
      {2,3,6},{2,5,10},{3,7,12},{3,8,4},{5,8,13},{5,9,12},
      {6,7,13},{7,10,4}}
   C: \alpha=(0 2 6 9)(1 3 8 10 11 12 13 7)(4 5)
      B_1={{0,1,2},{0,5,6},{0,11,12},{1,3,5},{1,8,10},{1,11,13},
      {2,5,10},{2,8,11},{3,9,13},{5,7,11},{5,8,13},{5,9,12},
      {6,7,13},{6,8,9}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,11},{2,9,5},{2,12,13},
 {3,7,12},{3,8,5},{3,9,13},{3,10,11},{4,8,12},{4,9,11},{4,10,13},{6,7,13},
 {6,8,9},{6,10,12},{6,11,5},{7,10,5}}
 I={{0,6},{1,3},{2,10},{4,5},{7,11},{8,13},{9,12}}
 Examples of antimorphisms:
   A: \alpha=(0 2 3 9)(1 5 11 10)(4 7 12 6)(8 13)
      B_1={{0,7,8},{0,9,10},{1,7,9},{1,8,10},{2,3,6},{2,4,7},
      {2,8,11},{2,9,5},{3,8,5},{6,7,13},{6,8,9},{6,10,12},
      {6,11,5},{7,10,5}}
   B: \alpha=(0 2 11 3)(1 6 10 7)(4 12 5 9)(8 13)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,8,10},
      {1,11,13},{1,12,5},{2,12,13},{3,9,13},{3,10,11},{4,9,11},
      {4,10,13},{7,10,5}}
   C: \alpha=(0 2 9 7 10 4 12 6 1 5 11 3)(8 13)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,5},{1,7,9},{1,11,13},
      {1,12,5},{2,12,13},{3,9,13},{3,10,11},{4,9,11},{4,10,13},
      {6,7,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 66 (fair: 4) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,10},{2,8,11},{2,9,6},{2,12,13},
 {3,7,12},{3,8,6},{3,9,13},{3,10,11},{4,5,6},{4,8,12},{4,9,11},{4,10,13},
 {5,7,11},{5,8,13},{5,9,12},{7,10,6}}
 I={{0,5},{1,4},{2,3},{7,13},{8,9},{10,12},{11,6}}
 Examples of antimorphisms:
   A: \alpha=(0 4 12 5 1 10)(2)(3 8 9)(6 11)(7 13)
      B_1={{0,9,10},{1,3,5},{2,4,7},{2,5,10},{2,8,11},{3,9,13},
      {3,10,11},{4,5,6},{4,8,12},{4,9,11},{4,10,13},{5,7,11},
      {5,8,13},{7,10,6}}
   B: \alpha=(0 5)(1 4)(2)(3)(6 11)(7 13)(8 9)(10 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},
      {1,7,9},{1,8,10},{1,11,13},{1,12,6},{2,8,11},{2,12,13},
      {3,7,12},{3,8,6}}
 # of antimorphisms of SASC-graph: 15 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,10},{2,8,11},{2,9,7},{2,12,13},
 {3,8,7},{3,9,13},{3,10,11},{4,5,7},{4,8,12},{4,9,11},{4,10,13},{5,8,13},
 {5,9,12},{6,8,9},{6,10,12},{6,11,7}}
 I={{0,8},{1,9},{2,4},{3,12},{5,11},{6,13},{10,7}}
 Examples of antimorphisms:
   A: \alpha=(0 1 12 4 3 2 13 10)(5 7 8 11 6 9)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,7},{1,11,13},{1,12,7},
      {2,9,7},{2,12,13},{3,8,7},{3,9,13},{3,10,11},{4,9,11},
      {5,9,12},{6,11,7}}
   B: \alpha=(0 2 11 9)(1 8 4 5)(3 10 12 7)(6 13)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
      {1,11,13},{1,12,7},{2,12,13},{3,9,13},{3,10,11},{4,8,12},
      {4,9,11},{4,10,13}}
   C: \alpha=(0 1 12 4)(2 13 10 3)(5 7 8 11 6 9)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,7},{1,11,13},{1,12,7},
      {2,9,7},{2,12,13},{3,8,7},{3,9,13},{3,10,11},{4,9,11},
      {5,9,12},{6,11,7}}
 # of antimorphisms of SASC-graph: 68 (fair: 4) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,10},{2,9,8},{2,12,13},
 {3,7,12},{3,9,13},{3,10,11},{4,5,8},{4,9,11},{4,10,13},{5,7,11},{5,9,12},
 {6,7,13},{6,10,12},{6,11,8},{7,10,8}}
 I={{0,7},{1,10},{2,11},{3,8},{4,12},{5,13},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 11)(2 7 9 13)(4 12)(5 10 8 6)
      B_1={{0,11,12},{0,13,8},{1,3,5},{1,7,9},{1,11,13},{1,12,8},
      {2,5,10},{2,9,8},{2,12,13},{3,7,12},{5,7,11},{5,9,12},
      {6,10,12},{6,11,8}}
   B: \alpha=(0 5 12 10)(1 7 13 4)(2 11)(3)(6 9)(8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,8},{1,4,6},
      {1,11,13},{1,12,8},{2,3,6},{2,9,8},{2,12,13},{3,7,12},
      {6,7,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 37 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,12,13},
 {3,7,12},{3,8,9},{3,10,11},{4,5,9},{4,8,12},{4,10,13},{5,7,11},{5,8,13},
 {6,7,13},{6,10,12},{6,11,9},{7,10,9}}
 I={{0,10},{1,7},{2,9},{3,13},{4,11},{5,12},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 3 8 5)(1 7)(2 12 4 9 13 6 10 11)
      B_1={{0,3,4},{1,3,5},{2,3,6},{2,4,7},{2,5,10},{2,12,13},
      {3,7,12},{3,10,11},{4,5,9},{4,10,13},{5,7,11},{5,8,13},
      {6,7,13},{7,10,9}}
   C: \alpha=(0 3 8 5)(1 7)(2 12 10 11)(4 9 13 6)
      B_1={{0,5,6},{1,3,5},{2,3,6},{2,4,7},{2,5,10},{2,12,13},
      {3,7,12},{3,8,9},{3,10,11},{4,5,9},{4,10,13},{5,7,11},
      {6,7,13},{7,10,9}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,8,11},{2,9,10},{2,12,13},
 {3,7,12},{3,8,10},{3,9,13},{4,5,10},{4,8,12},{4,9,11},{5,7,11},{5,8,13},
 {5,9,12},{6,7,13},{6,8,9},{6,11,10}}
 I={{0,9},{1,8},{2,5},{3,11},{4,13},{6,12},{7,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 11)(2 3 7 13)(4 9 8 10)(6 12)
      B_1={{0,1,2},{0,5,6},{0,7,8},{1,4,6},{1,7,9},{2,3,6},
      {2,4,7},{2,8,11},{2,9,10},{4,5,10},{5,7,11},{6,7,13},
      {6,8,9},{6,11,10}}
 # of antimorphisms of SASC-graph: 20 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,5,10},{2,9,11},{2,12,13},
 {3,7,12},{3,8,11},{3,9,13},{4,5,11},{4,8,12},{4,10,13},{5,8,13},{5,9,12},
 {6,7,13},{6,8,9},{6,10,12},{7,10,11}}
 I={{0,12},{1,13},{2,8},{3,10},{4,9},{5,7},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,9,12},
 {3,8,12},{3,9,13},{3,10,11},{4,5,12},{4,9,11},{4,10,13},{5,7,11},{5,8,13},
 {6,7,13},{6,8,9},{6,11,12},{7,10,12}}
 I={{0,11},{1,12},{2,13},{3,7},{4,8},{5,9},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 9)(2 4 12 10)(3 11 13 7 5 8)
      B_1={{0,1,2},{0,7,8},{1,7,9},{1,8,10},{1,11,13},{2,4,7},
      {2,8,11},{2,9,12},{3,8,12},{4,9,11},{5,7,11},{6,8,9},
      {6,11,12},{7,10,12}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,9,13},
 {3,7,12},{3,8,13},{3,10,11},{4,5,13},{4,8,12},{4,9,11},{5,7,11},{5,9,12},
 {6,8,9},{6,10,12},{6,11,13},{7,10,13}}
 I={{0,13},{1,11},{2,12},{3,9},{4,10},{5,8},{6,7}}
 Examples of antimorphisms:
   B: \alpha=(0 8 6 3)(1 11)(2 4 12 10)(5 7 9 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{1,8,10},{1,12,13},{2,4,7},{4,5,13},{6,8,9},
      {6,10,12},{7,10,13}}
   D: \alpha=(0 3 6 8)(1 11)(2 10 12 4)(5 13 9 7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{1,8,10},{1,12,13},{2,4,7},{4,5,13},{6,8,9},
      {6,10,12},{7,10,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,10},{2,8,11},{2,12,13},
 {3,7,12},{3,9,13},{3,10,11},{4,8,12},{4,9,11},{4,10,13},{5,7,11},{5,8,13},
 {5,9,12},{6,7,13},{6,8,9},{6,10,12}}
 I={{0,13},{1,12},{2,9},{3,8},{4,5},{6,11},{7,10}}
 Examples of antimorphisms:
   B: \alpha=(0 5 12 10)(1 7 13 4)(2 9)(3)(6 11)(8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,4,6},{2,3,6},
      {2,4,7},{2,5,10},{2,8,11},{2,12,13},{3,7,12},{4,8,12},
      {6,7,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 26 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,9},{2,10,0},{2,12,13},{3,7,12},{3,8,11},{3,9,0},{3,10,13},
 {4,5,0},{4,8,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},{6,7,13},
 {6,8,0},{6,9,12},{6,10,11},{7,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,9},{2,10,1},{2,12,13},{3,7,12},{3,8,11},{3,9,1},{3,10,13},
 {4,5,1},{4,8,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},{6,7,13},
 {6,8,1},{6,9,12},{6,10,11},{7,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,11},{3,9,2},{3,10,13},
 {4,5,2},{4,8,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},{6,7,13},
 {6,8,2},{6,9,12},{6,10,11},{7,11,2}}
 I={{0,1},{3,6},{4,7},{5,11},{8,9},{10,2},{12,13}}
 Examples of antimorphisms:
   B: \alpha=(0 8 3 12)(1 9 6 13)(2)(4 7)(5 11)(10)
      B_1={{0,3,4},{0,11,12},{1,4,6},{1,8,10},{1,11,13},{1,12,2},
      {3,8,11},{4,5,2},{4,8,13},{4,9,11},{4,10,12},{6,8,2},
      {6,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,9},{2,10,3},{2,12,13},
 {4,5,3},{4,8,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},{6,7,13},
 {6,8,3},{6,9,12},{6,10,11},{7,11,3}}
 I={{0,4},{1,5},{2,6},{7,12},{8,11},{9,3},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 5 9)(1 7 8 6)(3 4 12 11)(10 13)
      B_1={{0,1,2},{0,11,12},{0,13,3},{1,7,9},{1,8,10},{1,11,13},
      {1,12,3},{2,8,9},{2,12,13},{4,5,3},{4,8,13},{5,8,12},
      {5,9,13},{6,8,3}}
   B: \alpha=(0 3 4 9)(1 2 11 10)(5 6 8 13)(7 12)
      B_1={{0,1,2},{0,5,6},{0,11,12},{0,13,3},{1,4,6},{1,11,13},
      {1,12,3},{2,12,13},{4,8,13},{4,9,11},{4,10,12},{5,8,12},
      {6,9,12},{6,10,11}}
   C: \alpha=(0 5 13 3 4 8 6 9 1 2 11 10)(7 12)
      B_1={{0,1,2},{0,5,6},{0,11,12},{0,13,3},{1,4,6},{1,11,13},
      {1,12,3},{2,12,13},{4,8,13},{4,9,11},{4,10,12},{5,8,12},
      {6,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 76 (fair: 4) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,11},{2,8,9},{2,10,4},{2,12,13},
 {3,7,12},{3,8,11},{3,9,4},{3,10,13},{5,7,10},{5,8,12},{5,9,13},{6,7,13},
 {6,8,4},{6,9,12},{6,10,11},{7,11,4}}
 I={{0,3},{1,6},{2,7},{5,4},{8,13},{9,11},{10,12}}
 Examples of antimorphisms:
   C: \alpha=(0 11 4 3 1 13)(2 8 12 7 9 5 6 10)
      B_1={{0,11,12},{1,11,13},{2,3,6},{2,5,11},{2,8,9},{2,12,13},
      {3,7,12},{3,8,11},{3,9,4},{3,10,13},{5,9,13},{6,7,13},
      {6,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,9},{2,10,5},{2,12,13},
 {3,7,12},{3,8,11},{3,9,5},{3,10,13},{4,8,13},{4,9,11},{4,10,12},{6,7,13},
 {6,8,5},{6,9,12},{6,10,11},{7,11,5}}
 I={{0,6},{1,3},{2,11},{4,5},{7,10},{8,12},{9,13}}
 Examples of antimorphisms:
   A: \alpha=(0 4 7 12)(1 11 6 5)(2 10 8 3)(9 13)
      B_1={{0,3,4},{0,9,10},{1,4,6},{1,7,9},{1,12,5},{2,10,5},
      {3,7,12},{3,8,11},{3,9,5},{3,10,13},{4,9,11},{4,10,12},
      {6,9,12},{6,10,11}}
   B: \alpha=(0 2 9 12)(1 7 3 10)(4 5)(6 11 13 8)
      B_1={{0,1,2},{0,13,5},{1,8,10},{1,11,13},{1,12,5},{2,3,6},
      {2,10,5},{2,12,13},{3,7,12},{3,8,11},{3,9,5},{6,8,5},
      {6,9,12},{7,11,5}}
   C: \alpha=(0 4 7 1 11 6 5 12)(2 10 8 3)(9 13)
      B_1={{0,3,4},{0,9,10},{1,4,6},{1,7,9},{1,8,10},{1,12,5},
      {2,3,6},{3,7,12},{3,9,5},{3,10,13},{4,9,11},{4,10,12},
      {6,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 15 (fair: 5) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,9},{2,10,6},{2,12,13},
 {3,7,12},{3,8,11},{3,9,6},{3,10,13},{4,5,6},{4,8,13},{4,9,11},{4,10,12},
 {5,7,10},{5,8,12},{5,9,13},{7,11,6}}
 I={{0,5},{1,4},{2,3},{7,13},{8,6},{9,12},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,11},{2,8,9},{2,10,7},{2,12,13},
 {3,8,11},{3,9,7},{3,10,13},{4,5,7},{4,8,13},{4,9,11},{4,10,12},{5,8,12},
 {5,9,13},{6,8,7},{6,9,12},{6,10,11}}
 I={{0,8},{1,9},{2,4},{3,12},{5,10},{6,13},{11,7}}
 Examples of antimorphisms:
   A: \alpha=(0 6 2 12)(1 9)(3 7 10 4)(5 8 13 11)
      B_1={{0,9,10},{0,11,12},{0,13,7},{2,3,6},{2,5,11},{2,8,9},
      {3,9,7},{4,5,7},{4,8,13},{4,9,11},{4,10,12},{5,9,13},
      {6,8,7},{6,9,12}}
   B: \alpha=(0 8)(1 9)(2 4)(3 12)(5)(6 13)(7 11)(10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},
      {1,3,5},{1,4,6},{1,11,13},{1,12,7},{2,3,6},{2,5,11},
      {2,10,7},{3,10,13}}
 # of antimorphisms of SASC-graph: 19 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,11},{2,10,8},{2,12,13},
 {3,7,12},{3,9,8},{3,10,13},{4,5,8},{4,9,11},{4,10,12},{5,7,10},{5,9,13},
 {6,7,13},{6,9,12},{6,10,11},{7,11,8}}
 I={{0,7},{1,10},{2,9},{3,11},{4,13},{5,12},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 13 5 11)(2 4 10 9 7 12)(6 8)
      B_1={{0,1,2},{0,9,10},{0,13,8},{1,11,13},{1,12,8},{2,4,7},
      {2,5,11},{2,10,8},{3,7,12},{3,9,8},{3,10,13},{4,5,8},
      {5,7,10},{7,11,8}}
   B: \alpha=(0 2 4 11)(1 5 10 12)(3 7 9 13)(6 8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{2,3,6},{3,9,8},{3,10,13},{4,9,11},{4,10,12},
      {6,9,12},{6,10,11}}
   C: \alpha=(0 2 4 11)(1 7 3 5 10 13 9 12)(6 8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{2,3,6},{3,10,13},{4,9,11},{4,10,12},{6,7,13},
      {6,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 134 (fair: 10) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,10,9},{2,12,13},
 {3,7,12},{3,8,11},{3,10,13},{4,5,9},{4,8,13},{4,10,12},{5,7,10},{5,8,12},
 {6,7,13},{6,8,9},{6,10,11},{7,11,9}}
 I={{0,10},{1,7},{2,8},{3,9},{4,11},{5,13},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5 8 9)(2 3 7 13)(4 10 11)(6 12)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,12,9},{2,3,6},{2,4,7},
      {2,5,11},{2,10,9},{4,5,9},{4,10,12},{5,7,10},{5,8,12},
      {6,7,13},{7,11,9}}
   B: \alpha=(0)(1 5 8 9)(2 3 7 13)(4 11)(6 12)(10)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,12,9},{2,3,6},{2,4,7},
      {2,5,11},{2,10,9},{4,5,9},{4,10,12},{5,7,10},{5,8,12},
      {6,7,13},{7,11,9}}
   C: \alpha=(0 7 6 9)(1 12 11 5)(2 3 13 8 10 4)
      B_1={{0,1,2},{0,13,9},{1,8,10},{1,11,13},{1,12,9},{2,4,7},
      {2,5,11},{2,10,9},{2,12,13},{3,10,13},{5,7,10},{6,7,13},
      {6,10,11},{7,11,9}}
 # of antimorphisms of SASC-graph: 21 (fair: 3) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,5,11},{2,8,9},{2,12,13},
 {3,7,12},{3,8,11},{3,9,10},{4,5,10},{4,8,13},{4,9,11},{5,8,12},{5,9,13},
 {6,7,13},{6,8,10},{6,9,12},{7,11,10}}
 I={{0,9},{1,8},{2,10},{3,13},{4,12},{5,7},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 11)(2 12 7 6)(3 13)(4 9 8 10)
      B_1={{0,1,2},{0,7,8},{0,13,10},{1,7,9},{1,11,13},{2,3,6},
      {2,4,7},{2,5,11},{2,8,9},{3,7,12},{3,9,10},{4,5,10},
      {5,9,13},{7,11,10}}
 # of antimorphisms of SASC-graph: 10 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,8,9},{2,10,11},{2,12,13},
 {3,7,12},{3,9,11},{3,10,13},{4,5,11},{4,8,13},{4,10,12},{5,7,10},{5,8,12},
 {5,9,13},{6,7,13},{6,8,11},{6,9,12}}
 I={{0,12},{1,13},{2,5},{3,8},{4,9},{6,10},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 10)(2 6 11 9)(3 8)(4 12 13 7)
      B_1={{0,1,2},{0,7,8},{0,13,11},{1,8,10},{1,12,11},{2,3,6},
      {2,4,7},{2,10,11},{2,12,13},{3,7,12},{3,9,11},{4,5,11},
      {5,7,10},{5,8,12}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,9},{2,10,12},
 {3,8,11},{3,9,12},{3,10,13},{4,5,12},{4,8,13},{4,9,11},{5,7,10},{5,9,13},
 {6,7,13},{6,8,12},{6,10,11},{7,11,12}}
 I={{0,11},{1,12},{2,13},{3,7},{4,10},{5,8},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5 13 7)(2 3 12 8)(4 10 11)(6 9)
      B_1={{0,3,4},{0,5,6},{0,7,8},{1,3,5},{1,4,6},{1,8,10},
      {1,11,13},{2,8,9},{3,8,11},{3,9,12},{3,10,13},{4,8,13},
      {6,7,13},{6,10,11}}
   B: \alpha=(0)(1 5 13 7)(2 3 12 8)(4 10)(6 9)(11)
      B_1={{0,1,2},{0,9,10},{0,13,12},{1,7,9},{2,3,6},{2,4,7},
      {2,5,11},{2,10,12},{4,5,12},{4,9,11},{5,7,10},{5,9,13},
      {6,8,12},{7,11,12}}
 # of antimorphisms of SASC-graph: 27 (fair: 3) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,11},{2,8,9},{2,10,13},
 {3,7,12},{3,8,11},{3,9,13},{4,5,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},
 {6,8,13},{6,9,12},{6,10,11},{7,11,13}}
 I={{0,13},{1,11},{2,12},{3,10},{4,8},{5,9},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 8 5 10)(2 4 11 12 13 9)(6 7)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,7,9},{1,8,10},{2,4,7},
      {2,5,11},{2,10,13},{3,7,12},{3,8,11},{3,9,13},{4,5,13},
      {5,7,10},{7,11,13}}
   B: \alpha=(0 2 4 10)(1 5 11 9)(3 13 12 8)(6 7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,12,13},{2,3,6},{3,7,12},{3,8,11},{4,9,11},{4,10,12},
      {6,9,12},{6,10,11}}
   C: \alpha=(0 1 9 10 8 5)(2 7 3 13)(4 12 6 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{2,3,6},
      {2,4,7},{2,8,9},{3,8,11},{3,9,13},{4,9,11},{5,8,12},
      {6,8,13},{6,9,12}}
 # of antimorphisms of SASC-graph: 142 (fair: 10) 
 # of halving permutations: 12 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,9},{2,12,13},
 {3,7,12},{3,8,11},{3,10,13},{4,8,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},
 {5,9,13},{6,7,13},{6,9,12},{6,10,11}}
 I={{0,13},{1,12},{2,10},{3,9},{4,5},{6,8},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 3 1 6)(2 7 10)(4 5)(8 13 9 12)(11)
      B_1={{0,5,6},{1,3,5},{2,3,6},{2,4,7},{2,12,13},{3,7,12},
      {3,8,11},{3,10,13},{4,8,13},{4,9,11},{4,10,12},{6,7,13},
      {6,9,12},{6,10,11}}
   B: \alpha=(0 3 1 6)(2 10)(4 5)(7)(8 13 9 12)(11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{1,4,6},
      {1,7,9},{1,8,10},{1,11,13},{2,4,7},{2,5,11},{2,8,9},
      {5,8,12},{5,9,13}}
   C: \alpha=(0 7 13 3 11 9)(1 12)(2 5 4 10 8 6)
      B_1={{0,5,6},{0,7,8},{0,11,12},{2,3,6},{2,12,13},{3,7,12},
      {3,10,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},
      {6,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 27 (fair: 7) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 27 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,12},{2,9,13},{2,10,0},{3,7,13},{3,8,9},{3,10,12},{3,11,0},
 {4,5,10},{4,8,0},{4,9,11},{4,12,13},{5,7,12},{5,8,13},{5,9,0},{6,7,0},
 {6,8,11},{6,9,12},{6,10,13},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 1 13 8 2 7)(3 4 5 12 11 6)(9 10)
      B_1={{1,3,5},{1,8,10},{1,12,0},{2,4,7},{2,5,11},{2,10,0},
      {3,7,13},{3,10,12},{3,11,0},{4,5,10},{5,8,13},{6,8,11},
      {6,10,13},{7,10,11}}
   B: \alpha=(0 3 10 5)(1 2)(4 9 6 13)(7)(8)(11 12)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,13},{3,10,12},{4,8,0},{4,9,11},{5,7,12},{5,9,0},
      {6,8,11},{6,10,13}}
   C: \alpha=(0 3 13 4)(1 2)(5 9 6 11 7 12 8 10)
      B_1={{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,9,13},{2,10,0},
      {3,8,9},{3,10,12},{3,11,0},{4,5,10},{4,9,11},{4,12,13},
      {6,9,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 47 (fair: 19) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,12},{2,9,13},{2,10,1},{3,7,13},{3,8,9},{3,10,12},{3,11,1},
 {4,5,10},{4,8,1},{4,9,11},{4,12,13},{5,7,12},{5,8,13},{5,9,1},{6,7,1},
 {6,8,11},{6,9,12},{6,10,13},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 8 9 11)(2)(3 5)(4 6)(7 13 12 10)
      B_1={{0,3,4},{0,7,8},{0,11,12},{2,4,7},{2,5,11},{2,8,12},
      {4,5,10},{4,8,1},{4,9,11},{4,12,13},{5,7,12},{5,8,13},
      {5,9,1},{7,10,11}}
   C: \alpha=(0 9 8 13)(1 10 11 4)(2 7 6 12)(3 5)
      B_1={{0,3,4},{0,13,1},{2,3,6},{2,4,7},{2,9,13},{2,10,1},
      {3,7,13},{3,8,9},{3,10,12},{3,11,1},{4,9,11},{6,8,11},
      {6,9,12},{6,10,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,13},{3,8,9},{3,10,12},{3,11,2},
 {4,5,10},{4,8,2},{4,9,11},{4,12,13},{5,7,12},{5,8,13},{5,9,2},{6,7,2},
 {6,8,11},{6,9,12},{6,10,13},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,11},{8,12},{9,13},{10,2}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,12},{2,9,13},{2,10,3},
 {4,5,10},{4,8,3},{4,9,11},{4,12,13},{5,7,12},{5,8,13},{5,9,3},{6,7,3},
 {6,8,11},{6,9,12},{6,10,13},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,13},{8,9},{10,12},{11,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,11},{2,8,12},{2,9,13},{2,10,4},
 {3,7,13},{3,8,9},{3,10,12},{3,11,4},{5,7,12},{5,8,13},{5,9,4},{6,7,4},
 {6,8,11},{6,9,12},{6,10,13},{7,10,11}}
 I={{0,3},{1,6},{2,7},{5,10},{8,4},{9,11},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 9 8)(1 10 3 7)(4 6 5 11)(12 13)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,13,4},{1,3,5},{1,7,9},
      {1,12,4},{2,9,13},{2,10,4},{3,10,12},{3,11,4},{5,7,12},
      {5,8,13},{5,9,4}}
   B: \alpha=(0 5 3 10)(1 12 8 11)(2 7)(4 9 6 13)
      B_1={{0,1,2},{0,5,6},{0,11,12},{0,13,4},{1,11,13},{2,3,6},
      {2,5,11},{2,8,12},{2,9,13},{2,10,4},{3,8,9},{3,10,12},
      {3,11,4},{6,9,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,12},{2,9,13},{2,10,5},
 {3,7,13},{3,8,9},{3,10,12},{3,11,5},{4,8,5},{4,9,11},{4,12,13},{6,7,5},
 {6,8,11},{6,9,12},{6,10,13},{7,10,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,12},{8,13},{9,5}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,12},{2,9,13},{2,10,6},
 {3,7,13},{3,8,9},{3,10,12},{3,11,6},{4,5,10},{4,8,6},{4,9,11},{4,12,13},
 {5,7,12},{5,8,13},{5,9,6},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,6},{8,11},{9,12},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,11},{2,8,12},{2,9,13},{2,10,7},
 {3,8,9},{3,10,12},{3,11,7},{4,5,10},{4,8,7},{4,9,11},{4,12,13},{5,8,13},
 {5,9,7},{6,8,11},{6,9,12},{6,10,13}}
 I={{0,8},{1,9},{2,4},{3,13},{5,12},{6,7},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,11},{2,9,13},{2,10,8},
 {3,7,13},{3,10,12},{3,11,8},{4,5,10},{4,9,11},{4,12,13},{5,7,12},{5,9,8},
 {6,7,8},{6,9,12},{6,10,13},{7,10,11}}
 I={{0,7},{1,10},{2,12},{3,9},{4,8},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 9)(2 6 7 10)(3 12 11 13)(4 8)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,3,6},{2,4,7},{2,5,11},{3,7,13},{4,5,10},{4,9,11},
      {4,12,13},{7,10,11}}
   B: \alpha=(0 7)(1 4 10 8)(2 9 6 5)(3 11 13 12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},
      {1,3,5},{1,4,6},{1,11,13},{2,3,6},{2,9,13},{2,10,8},
      {3,10,12},{6,10,13}}
   C: \alpha=(0 7)(1 5 2 8 3 12)(4 13 11 10 9 6)
      B_1={{1,7,9},{1,12,8},{2,4,7},{2,5,11},{3,7,13},{3,11,8},
      {4,5,10},{4,12,13},{5,7,12},{5,9,8},{6,7,8},{6,9,12},
      {6,10,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 38 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,10,9},
 {3,7,13},{3,10,12},{3,11,9},{4,5,10},{4,8,9},{4,12,13},{5,7,12},{5,8,13},
 {6,7,9},{6,8,11},{6,10,13},{7,10,11}}
 I={{0,10},{1,7},{2,13},{3,8},{4,11},{5,9},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 8)(2 5 10 7)(3 13 9 12)(4 11)
      B_1={{0,1,2},{0,11,12},{0,13,9},{1,8,10},{1,11,13},{2,3,6},
      {2,4,7},{2,8,12},{2,10,9},{3,10,12},{3,11,9},{4,5,10},
      {6,8,11},{6,10,13}}
   C: \alpha=(0 1 6 10 5 8 4 13 9 12 2 7 3 11)
      B_1={{0,3,4},{0,5,6},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
      {2,3,6},{2,5,11},{2,8,12},{2,10,9},{3,7,13},{4,5,10},
      {4,8,9},{6,7,9}}
 # of antimorphisms of SASC-graph: 18 (fair: 0) 
 # of halving permutations: 8 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,9,13},
 {3,7,13},{3,8,9},{3,11,10},{4,8,10},{4,9,11},{4,12,13},{5,7,12},{5,8,13},
 {5,9,10},{6,7,10},{6,8,11},{6,9,12}}
 I={{0,9},{1,8},{2,10},{3,12},{4,5},{6,13},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 7 3 10)(1 5 2 8 13 9)(4 11 12 6)
      B_1={{0,5,6},{0,7,8},{1,7,9},{2,5,11},{3,8,9},{3,11,10},
      {4,8,10},{4,9,11},{5,7,12},{5,8,13},{5,9,10},{6,7,10},
      {6,8,11},{6,9,12}}
   B: \alpha=(0 4 9 5)(1 11 10 6)(2 13 8 7)(3 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{1,3,5},{1,4,6},{2,3,6},
      {2,5,11},{2,8,12},{2,9,13},{3,8,9},{3,11,10},{4,8,10},
      {5,9,10},{6,8,11}}
   C: \alpha=(0 7 3 11 12 6 4 10)(1 5 2 8 13 9)
      B_1={{0,5,6},{0,7,8},{1,7,9},{2,5,11},{3,8,9},{3,11,10},
      {4,8,10},{4,9,11},{5,7,12},{5,8,13},{5,9,10},{6,7,10},
      {6,8,11},{6,9,12}}
 # of antimorphisms of SASC-graph: 9 (fair: 3) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,8,12},{2,9,13},{2,10,11},
 {3,7,13},{3,8,9},{3,10,12},{4,5,10},{4,8,11},{4,12,13},{5,7,12},{5,8,13},
 {5,9,11},{6,7,11},{6,9,12},{6,10,13}}
 I={{0,12},{1,13},{2,5},{3,11},{4,9},{6,8},{7,10}}
 Examples of antimorphisms:
   C: \alpha=(0 12)(1 6 3 8 4 2 9 11 7 13 5 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},
      {1,8,10},{2,3,6},{2,9,13},{2,10,11},{4,8,11},{5,8,13},
      {6,7,11},{6,10,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,9,13},{2,10,12},
 {3,7,13},{3,8,9},{3,11,12},{4,5,10},{4,8,12},{4,9,11},{5,8,13},{5,9,12},
 {6,7,12},{6,8,11},{6,10,13},{7,10,11}}
 I={{0,11},{1,12},{2,8},{3,10},{4,13},{5,7},{6,9}}
 Examples of antimorphisms:
   C: \alpha=(0 10 4 2 3 12)(1 6 11 13 9 8)(5 7)
      B_1={{0,5,6},{0,13,12},{1,3,5},{1,8,10},{2,3,6},{2,5,11},
      {2,9,13},{2,10,12},{4,5,10},{4,8,12},{5,8,13},{5,9,12},
      {6,8,11},{6,10,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,10,13},
 {3,8,9},{3,10,12},{3,11,13},{4,5,10},{4,8,13},{4,9,11},{5,7,12},{5,9,13},
 {6,7,13},{6,8,11},{6,9,12},{7,10,11}}
 I={{0,13},{1,11},{2,9},{3,7},{4,12},{5,8},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 12)(2 6 13 11)(3 7)(4 9 10 8)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,4,7},{2,5,11},{2,10,13},{3,10,12},{4,5,10},{4,8,13},
      {6,7,13},{7,10,11}}
   B: \alpha=(0 10 8 12)(1 2 11 9)(3 7)(4 13 6 5)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{1,3,5},
      {1,4,6},{2,3,6},{2,8,12},{3,8,9},{3,11,13},{4,8,13},
      {4,9,11},{6,8,11}}
   C: \alpha=(0 9 7 13 5 12)(1 6 8 2)(3 4 11 10)
      B_1={{0,11,12},{1,4,6},{1,7,9},{1,8,10},{1,12,13},{2,8,12},
      {2,10,13},{3,8,9},{3,10,12},{3,11,13},{4,8,13},{4,9,11},
      {5,9,13},{6,9,12}}
 # of antimorphisms of SASC-graph: 48 (fair: 2) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,9,13},
 {3,7,13},{3,8,9},{3,10,12},{4,5,10},{4,9,11},{4,12,13},{5,7,12},{5,8,13},
 {6,8,11},{6,9,12},{6,10,13},{7,10,11}}
 I={{0,13},{1,12},{2,10},{3,11},{4,8},{5,9},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 1 6 11)(2 5 13 12)(3 10 9 7)(4 8)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,3,6},{2,8,12},{2,9,13},{3,7,13},{3,8,9},{4,9,11},
      {5,8,13},{6,9,12}}
   B: \alpha=(0 5 13 9)(1 12)(2 7 11 8)(3 4 10 6)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{1,8,10},{1,11,13},{2,4,7},{3,7,13},{5,8,13},
      {6,8,11},{6,10,13}}
   C: \alpha=(0 3 9 5 10 1 2 6 12 7 11 13)(4 8)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{1,4,6},{2,4,7},
      {2,5,11},{2,9,13},{3,10,12},{4,5,10},{4,9,11},{4,12,13},
      {6,9,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 10 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 28 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,12},{2,9,0},{2,10,13},{3,7,13},{3,8,9},{3,10,12},{3,11,0},
 {4,5,10},{4,8,0},{4,9,11},{4,12,13},{5,7,0},{5,8,13},{5,9,12},{6,7,12},
 {6,8,11},{6,9,13},{6,10,0},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 7 9 12)(1 2)(3)(4)(5 6)(8 10 11 13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,7,13},{3,10,12},{4,8,0},{4,9,11},{6,7,12},{6,8,11},
      {6,9,13},{6,10,0}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,12},{2,9,1},{2,10,13},{3,7,13},{3,8,9},{3,10,12},{3,11,1},
 {4,5,10},{4,8,1},{4,9,11},{4,12,13},{5,7,1},{5,8,13},{5,9,12},{6,7,12},
 {6,8,11},{6,9,13},{6,10,1},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,13},{3,8,9},{3,10,12},{3,11,2},
 {4,5,10},{4,8,2},{4,9,11},{4,12,13},{5,7,2},{5,8,13},{5,9,12},{6,7,12},
 {6,8,11},{6,9,13},{6,10,2},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,11},{8,12},{9,2},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,12},{2,9,3},{2,10,13},
 {4,5,10},{4,8,3},{4,9,11},{4,12,13},{5,7,3},{5,8,13},{5,9,12},{6,7,12},
 {6,8,11},{6,9,13},{6,10,3},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,13},{8,9},{10,12},{11,3}}
 Examples of antimorphisms:
   A: \alpha=(0 2 6)(1 5)(3 7 9 12)(4)(8 10 11 13)
      B_1={{0,5,6},{0,7,8},{0,11,12},{2,4,7},{2,5,11},{2,8,12},
      {4,5,10},{4,12,13},{5,7,3},{5,8,13},{5,9,12},{6,7,12},
      {6,8,11},{7,10,11}}
   B: \alpha=(0)(1 5)(2 6)(3 7 9 12)(4)(8 10 11 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,3},{2,9,3},{2,10,13},{4,8,3},{4,9,11},
      {6,9,13},{6,10,3}}
   C: \alpha=(0 9 2 11)(1 10 3 4)(5 12 8 6)(7 13)
      B_1={{0,7,8},{0,9,10},{1,7,9},{1,8,10},{2,4,7},{2,5,11},
      {4,5,10},{4,8,3},{4,9,11},{5,7,3},{5,9,12},{6,7,12},
      {6,8,11},{7,10,11}}
 # of antimorphisms of SASC-graph: 15 (fair: 3) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,11},{2,8,12},{2,9,4},{2,10,13},
 {3,7,13},{3,8,9},{3,10,12},{3,11,4},{5,7,4},{5,8,13},{5,9,12},{6,7,12},
 {6,8,11},{6,9,13},{6,10,4},{7,10,11}}
 I={{0,3},{1,6},{2,7},{5,10},{8,4},{9,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,12},{2,9,5},{2,10,13},
 {3,7,13},{3,8,9},{3,10,12},{3,11,5},{4,8,5},{4,9,11},{4,12,13},{6,7,12},
 {6,8,11},{6,9,13},{6,10,5},{7,10,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,5},{8,13},{9,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 11 6 9 8)(2 13 3 12)(4 10)(5 7)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{1,7,9},{1,11,13},
      {2,4,7},{2,8,12},{3,7,13},{4,9,11},{4,12,13},{6,7,12},
      {6,9,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,12},{2,9,6},{2,10,13},
 {3,7,13},{3,8,9},{3,10,12},{3,11,6},{4,5,10},{4,8,6},{4,9,11},{4,12,13},
 {5,7,6},{5,8,13},{5,9,12},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,12},{8,11},{9,13},{10,6}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,11},{2,8,12},{2,9,7},{2,10,13},
 {3,8,9},{3,10,12},{3,11,7},{4,5,10},{4,8,7},{4,9,11},{4,12,13},{5,8,13},
 {5,9,12},{6,8,11},{6,9,13},{6,10,7}}
 I={{0,8},{1,9},{2,4},{3,13},{5,7},{6,12},{10,11}}
 Examples of antimorphisms:
   B: \alpha=(0 8)(1 9)(2 4)(3 13)(5)(6 12)(7)(10 11)
      B_1={{0,1,2},{0,13,7},{1,8,10},{1,11,13},{2,3,6},{2,5,11},
      {2,8,12},{2,9,7},{2,10,13},{5,8,13},{5,9,12},{6,8,11},
      {6,9,13},{6,10,7}}
 # of antimorphisms of SASC-graph: 1 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,11},{2,9,8},{2,10,13},
 {3,7,13},{3,10,12},{3,11,8},{4,5,10},{4,9,11},{4,12,13},{5,7,8},{5,9,12},
 {6,7,12},{6,9,13},{6,10,8},{7,10,11}}
 I={{0,7},{1,10},{2,12},{3,9},{4,8},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 2 5 8)(1 10)(3 11 12 13)(4 7 9 6)
      B_1={{0,9,10},{0,13,8},{2,4,7},{2,5,11},{2,9,8},{2,10,13},
      {3,10,12},{3,11,8},{4,5,10},{4,9,11},{4,12,13},{6,9,13},
      {6,10,8},{7,10,11}}
   B: \alpha=(0 4 7 8)(1)(2 5 9 6)(3 11 12 13)(10)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,8},{1,7,9},{1,11,13},
      {2,3,6},{2,4,7},{2,9,8},{2,10,13},{3,7,13},{4,9,11},
      {5,9,12},{7,10,11}}
   C: \alpha=(0 1 5 9)(2 6 7 10)(3 12 11 13)(4 8)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,5,11},{2,10,13},{3,7,13},{4,5,10},{4,9,11},{4,12,13},
      {6,7,12},{6,10,8}}
   D: \alpha=(0 8 7 4)(1 10)(2 6 9 5)(3 13 12 11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,7,9},{1,11,13},{1,12,8},{2,3,6},{3,7,13},{5,7,8},
      {5,9,12},{6,7,12}}
 # of antimorphisms of SASC-graph: 44 (fair: 4) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,10,13},
 {3,7,13},{3,10,12},{3,11,9},{4,5,10},{4,8,9},{4,12,13},{5,7,9},{5,8,13},
 {6,7,12},{6,8,11},{6,10,9},{7,10,11}}
 I={{0,10},{1,7},{2,9},{3,8},{4,11},{5,12},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 5 7)(1 11 3 10 13 8)(4 9 12 6)
      B_1={{0,7,8},{0,11,12},{1,8,10},{2,4,7},{2,5,11},{2,8,12},
      {2,10,13},{3,11,9},{4,5,10},{4,8,9},{6,7,12},{6,8,11},
      {6,10,9},{7,10,11}}
   C: \alpha=(0 6 7 4 5 12 2 10)(1 9 8 13 11 3)
      B_1={{0,5,6},{0,11,12},{1,3,5},{1,4,6},{1,8,10},{1,11,13},
      {2,4,7},{2,8,12},{3,10,12},{4,8,9},{4,12,13},{6,8,11},
      {6,10,9},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,9,10},
 {3,7,13},{3,8,9},{3,11,10},{4,8,10},{4,9,11},{4,12,13},{5,7,10},{5,8,13},
 {5,9,12},{6,7,12},{6,8,11},{6,9,13}}
 I={{0,9},{1,8},{2,13},{3,12},{4,5},{6,10},{7,11}}
 Examples of antimorphisms:
   B: \alpha=(0 4 6 7)(1 12 8 3)(2 13)(5 10 11 9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,10},{1,3,5},
      {2,3,6},{2,8,12},{2,9,10},{3,11,10},{5,9,12},{6,7,12},
      {6,8,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,8,12},{2,9,11},{2,10,13},
 {3,7,13},{3,8,9},{3,10,12},{4,5,10},{4,8,11},{4,12,13},{5,7,11},{5,8,13},
 {5,9,12},{6,7,12},{6,9,13},{6,10,11}}
 I={{0,12},{1,13},{2,5},{3,11},{4,9},{6,8},{7,10}}
 Examples of antimorphisms:
   B: \alpha=(0 6 9 7)(1 13)(2 11 5 3)(4 10 12 8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{1,3,5},{1,4,6},{1,7,9},
      {1,8,10},{1,12,11},{2,4,7},{2,8,12},{2,9,11},{4,5,10},
      {5,9,12},{6,7,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,9,12},{2,10,13},
 {3,7,13},{3,8,9},{3,11,12},{4,5,10},{4,8,12},{4,9,11},{5,7,12},{5,8,13},
 {6,8,11},{6,9,13},{6,10,12},{7,10,11}}
 I={{0,11},{1,12},{2,8},{3,10},{4,13},{5,9},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 13)(2 6 4 10)(3 12 5 8 11 9)
      B_1={{0,7,8},{0,9,10},{0,13,12},{1,4,6},{1,7,9},{1,8,10},
      {2,9,12},{2,10,13},{3,8,9},{4,8,12},{5,7,12},{6,8,11},
      {6,9,13},{6,10,12}}
   B: \alpha=(0 5 11 9)(1 7 8 13)(2 4 12 6)(3 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,3,5},{1,4,6},
      {1,8,10},{1,11,13},{2,3,6},{3,8,9},{3,11,12},{4,8,12},
      {4,9,11},{6,8,11}}
   C: \alpha=(0 2 5 7 8 12)(1 11 9 6)(3 10)(4 13)
      B_1={{0,1,2},{0,3,4},{0,9,10},{1,3,5},{1,4,6},{1,7,9},
      {1,8,10},{2,4,7},{2,9,12},{3,8,9},{4,5,10},{4,8,12},
      {4,9,11},{5,7,12}}
 # of antimorphisms of SASC-graph: 44 (fair: 2) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,9,13},
 {3,8,9},{3,10,12},{3,11,13},{4,5,10},{4,8,13},{4,9,11},{5,7,13},{5,9,12},
 {6,7,12},{6,8,11},{6,10,13},{7,10,11}}
 I={{0,13},{1,11},{2,10},{3,7},{4,12},{5,8},{6,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,10,13},
 {3,7,13},{3,8,9},{3,10,12},{4,5,10},{4,9,11},{4,12,13},{5,8,13},{5,9,12},
 {6,7,12},{6,8,11},{6,9,13},{7,10,11}}
 I={{0,13},{1,12},{2,9},{3,11},{4,8},{5,7},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 5 9 8)(1 10 13 12 3 7)(2 4 11 6)
      B_1={{0,7,8},{0,9,10},{0,11,12},{1,7,9},{2,4,7},{2,5,11},
      {2,8,12},{2,10,13},{3,10,12},{4,5,10},{5,9,12},{6,7,12},
      {6,8,11},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 29 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,12},{2,9,0},{2,10,13},{3,7,0},{3,8,11},{3,9,13},{3,10,12},
 {4,5,10},{4,8,9},{4,11,0},{4,12,13},{5,7,13},{5,8,0},{5,9,12},{6,7,12},
 {6,8,13},{6,9,11},{6,10,0},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,12},{2,9,1},{2,10,13},{3,7,1},{3,8,11},{3,9,13},{3,10,12},
 {4,5,10},{4,8,9},{4,11,1},{4,12,13},{5,7,13},{5,8,1},{5,9,12},{6,7,12},
 {6,8,13},{6,9,11},{6,10,1},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 5 7 11)(1 4 3 9)(2 12 6 13)(8 10)
      B_1={{0,5,6},{0,9,10},{2,4,7},{2,5,11},{2,8,12},{3,9,13},
      {4,5,10},{4,8,9},{4,11,1},{4,12,13},{5,9,12},{6,8,13},
      {6,9,11},{7,10,11}}
 # of antimorphisms of SASC-graph: 10 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,12},{2,9,3},{2,10,13},
 {4,5,10},{4,8,9},{4,11,3},{4,12,13},{5,7,13},{5,8,3},{5,9,12},{6,7,12},
 {6,8,13},{6,9,11},{6,10,3},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,3},{8,11},{9,13},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 5 3 11 10 13)(2 8 4 6 12 9)
      B_1={{0,1,2},{0,11,12},{1,4,6},{1,11,13},{1,12,3},{2,4,7},
      {2,5,11},{2,8,12},{2,10,13},{4,5,10},{4,11,3},{4,12,13},
      {5,7,13},{5,9,12}}
 # of antimorphisms of SASC-graph: 16 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=3 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,11},{2,8,12},{2,9,4},{2,10,13},
 {3,7,4},{3,8,11},{3,9,13},{3,10,12},{5,7,13},{5,8,4},{5,9,12},{6,7,12},
 {6,8,13},{6,9,11},{6,10,4},{7,10,11}}
 I={{0,3},{1,6},{2,7},{5,10},{8,9},{11,4},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,12},{2,9,6},{2,10,13},
 {3,7,6},{3,8,11},{3,9,13},{3,10,12},{4,5,10},{4,8,9},{4,11,6},{4,12,13},
 {5,7,13},{5,8,6},{5,9,12},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,12},{8,13},{9,11},{10,6}}
 Examples of antimorphisms:
   C: \alpha=(0 4 13 10 9 8)(1 11 7 3)(2 6 5 12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,7,9},
      {1,11,13},{1,12,6},{2,9,6},{3,7,6},{3,9,13},{4,12,13},
      {5,7,13},{5,9,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,11},{2,9,8},{2,10,13},
 {3,7,8},{3,9,13},{3,10,12},{4,5,10},{4,11,8},{4,12,13},{5,7,13},{5,9,12},
 {6,7,12},{6,9,11},{6,10,8},{7,10,11}}
 I={{0,7},{1,10},{2,12},{3,11},{4,9},{5,8},{6,13}}
 Examples of antimorphisms:
   B: \alpha=(0 5 12 1)(2 10 7 8)(3 11)(4 6 9 13)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,8},{1,4,6},{2,3,6},
      {2,10,13},{3,7,8},{3,9,13},{3,10,12},{5,7,13},{5,9,12},
      {6,7,12},{6,10,8}}
   C: \alpha=(0 1 13 9)(2 8 7 10)(3 11)(4 12 5 6)
      B_1={{0,9,10},{0,11,12},{0,13,8},{1,4,6},{1,11,13},{1,12,8},
      {2,3,6},{2,10,13},{3,7,8},{3,10,12},{5,9,12},{6,7,12},
      {6,9,11},{6,10,8}}
   D: \alpha=(0 1 12 5)(2 8 7 10)(3 11)(4 13 9 6)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,8},{1,4,6},{2,3,6},
      {2,10,13},{3,7,8},{3,9,13},{3,10,12},{5,7,13},{5,9,12},
      {6,7,12},{6,10,8}}
 # of antimorphisms of SASC-graph: 12 (fair: 6) 
 # of halving permutations: 9 (fair: 3; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,10,13},
 {3,7,9},{3,8,11},{3,10,12},{4,5,10},{4,11,9},{4,12,13},{5,7,13},{5,8,9},
 {6,7,12},{6,8,13},{6,10,9},{7,10,11}}
 I={{0,10},{1,7},{2,9},{3,13},{4,8},{5,12},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 2 6 1 3 11)(4 5 13 9)(7 8 12 10)
      B_1={{0,1,2},{1,4,6},{1,8,10},{1,11,13},{1,12,9},{2,4,7},
      {2,5,11},{2,8,12},{2,10,13},{3,8,11},{4,11,9},{4,12,13},
      {5,7,13},{7,10,11}}
   B: \alpha=(0)(1 9 4 13)(2 8 3 7)(5 12)(6 11)(10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{1,4,6},{1,12,9},{2,3,6},
      {2,8,12},{2,10,13},{3,7,9},{3,10,12},{4,12,13},{6,7,12},
      {6,8,13},{6,10,9}}
   C: \alpha=(0 3 10 7 5 6 2 13)(1 9 4 12 11 8)
      B_1={{0,7,8},{0,13,9},{1,12,9},{2,3,6},{2,8,12},{3,7,9},
      {3,8,11},{3,10,12},{4,12,13},{5,7,13},{5,8,9},{6,7,12},
      {6,8,13},{6,10,9}}
   D: \alpha=(0 3 10 13)(1 7)(2 9)(4 12 8 5)(6)(11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,11,12},{1,4,6},{1,8,10},
      {2,3,6},{2,4,7},{2,5,11},{2,8,12},{2,10,13},{4,5,10},
      {6,8,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 30 (fair: 12) 
 # of halving permutations: 8 (fair: 2; strong: 0) 


 System No. 30 
 |Aut(S)|=2 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,12},{2,10,0},{3,7,13},{3,8,9},{3,10,12},{3,11,0},
 {4,5,10},{4,8,11},{4,9,0},{4,12,13},{5,7,12},{5,8,0},{5,9,13},{6,7,0},
 {6,8,12},{6,9,11},{6,10,13},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 13)(1)(2)(3 4)(5 6)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,6},{2,8,13},{2,9,12},
      {3,8,9},{3,11,0},{4,8,11},{4,9,0},{5,8,0},{5,9,13},
      {6,8,12},{6,9,11}}
   C: \alpha=(0 1 13)(2)(3 4)(5 8 10 6 7 9)(11 12)
      B_1={{1,4,6},{1,8,10},{1,12,0},{2,3,6},{2,8,13},{2,9,12},
      {3,8,9},{4,8,11},{4,9,0},{4,12,13},{5,9,13},{6,7,0},
      {6,8,12},{6,9,11}}
 # of antimorphisms of SASC-graph: 3 (fair: 1) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,12},{2,10,1},{3,7,13},{3,8,9},{3,10,12},{3,11,1},
 {4,5,10},{4,8,11},{4,9,1},{4,12,13},{5,7,12},{5,8,1},{5,9,13},{6,7,1},
 {6,8,12},{6,9,11},{6,10,13},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,13},{3,8,9},{3,10,12},{3,11,2},
 {4,5,10},{4,8,11},{4,9,2},{4,12,13},{5,7,12},{5,8,2},{5,9,13},{6,7,2},
 {6,8,12},{6,9,11},{6,10,13},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,11},{8,13},{9,12},{10,2}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,13},{2,9,12},{2,10,3},
 {4,5,10},{4,8,11},{4,9,3},{4,12,13},{5,7,12},{5,8,3},{5,9,13},{6,7,3},
 {6,8,12},{6,9,11},{6,10,13},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,13},{8,9},{10,12},{11,3}}
 Examples of antimorphisms:
   A: \alpha=(0 5 12 13)(1 9 3 10 8 2)(4 11 6 7)
      B_1={{0,5,6},{0,9,10},{1,7,9},{2,4,7},{2,5,11},{2,8,13},
      {2,9,12},{2,10,3},{4,5,10},{4,12,13},{5,9,13},{6,9,11},
      {6,10,13},{7,10,11}}
   C: \alpha=(0 7 5 6 3 8 12 1 10 13)(2 11 9 4)
      B_1={{0,5,6},{0,7,8},{1,4,6},{1,7,9},{1,11,13},{1,12,3},
      {2,4,7},{2,8,13},{4,8,11},{4,12,13},{5,8,3},{6,9,11},
      {6,10,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,11},{2,8,13},{2,9,12},{2,10,4},
 {3,7,13},{3,8,9},{3,10,12},{3,11,4},{5,7,12},{5,8,4},{5,9,13},{6,7,4},
 {6,8,12},{6,9,11},{6,10,13},{7,10,11}}
 I={{0,3},{1,6},{2,7},{5,10},{8,11},{9,4},{12,13}}
 Examples of antimorphisms:
   B: \alpha=(0 5 3 10)(1 12 9 11)(2 7)(4 8 6 13)
      B_1={{0,1,2},{0,5,6},{0,11,12},{0,13,4},{1,11,13},{2,3,6},
      {2,5,11},{2,8,13},{2,9,12},{2,10,4},{3,8,9},{3,10,12},
      {3,11,4},{6,8,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},{2,10,6},
 {3,7,13},{3,8,9},{3,10,12},{3,11,6},{4,5,10},{4,8,11},{4,9,6},{4,12,13},
 {5,7,12},{5,8,6},{5,9,13},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,6},{8,12},{9,11},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,10,9},
 {3,7,13},{3,10,12},{3,11,9},{4,5,10},{4,8,11},{4,12,13},{5,7,12},{5,8,9},
 {6,7,9},{6,8,12},{6,10,13},{7,10,11}}
 I={{0,10},{1,7},{2,12},{3,8},{4,9},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 2 7 6)(1 11 9 5)(3 13 10 8 4 12)
      B_1={{0,1,2},{0,7,8},{0,11,12},{0,13,9},{1,8,10},{1,11,13},
      {1,12,9},{2,8,13},{3,7,13},{4,12,13},{5,7,12},{5,8,9},
      {6,7,9},{6,8,12}}
   B: \alpha=(0 10)(1 7)(2 12)(3 8)(4 9)(5 13)(6)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},
      {1,4,6},{1,11,13},{1,12,9},{2,3,6},{2,8,13},{3,7,13},
      {3,11,9},{4,12,13}}
 # of antimorphisms of SASC-graph: 13 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},
 {3,7,13},{3,8,9},{3,11,10},{4,8,11},{4,9,10},{4,12,13},{5,7,12},{5,8,10},
 {5,9,13},{6,7,10},{6,8,12},{6,9,11}}
 I={{0,9},{1,8},{2,10},{3,12},{4,5},{6,13},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 13 5)(2 11 9 10 3 8)(4 12 7 6)
      B_1={{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,11,13},{1,12,10},
      {2,8,13},{3,11,10},{4,8,11},{4,12,13},{5,8,10},{6,7,10},
      {6,8,12},{6,9,11}}
   C: \alpha=(0 1 13 5 6 4 12 7)(2 11 9 10 3 8)
      B_1={{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,11,13},{1,12,10},
      {2,8,13},{3,11,10},{4,8,11},{4,12,13},{5,8,10},{6,7,10},
      {6,8,12},{6,9,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,8,13},{2,9,12},{2,10,11},
 {3,7,13},{3,8,9},{3,10,12},{4,5,10},{4,9,11},{4,12,13},{5,7,12},{5,8,11},
 {5,9,13},{6,7,11},{6,8,12},{6,10,13}}
 I={{0,12},{1,13},{2,5},{3,11},{4,8},{6,9},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 31 
 |Aut(S)|=4 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,12},{2,10,0},{3,7,13},{3,8,11},{3,9,0},{3,10,12},
 {4,5,10},{4,8,9},{4,11,0},{4,12,13},{5,7,12},{5,8,0},{5,9,13},{6,7,0},
 {6,8,12},{6,9,11},{6,10,13},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 2 12 3)(1 5 8 13)(4 6 7 11)(9 10)
      B_1={{1,7,9},{1,11,13},{1,12,0},{2,10,0},{3,10,12},{4,8,9},
      {4,11,0},{4,12,13},{5,7,12},{5,8,0},{5,9,13},{6,7,0},
      {6,8,12},{6,9,11}}
   B: \alpha=(0 13)(1)(2)(3 4)(5 6)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,6},{2,8,13},{2,9,12},
      {3,8,11},{3,9,0},{4,8,9},{4,11,0},{5,8,0},{5,9,13},
      {6,8,12},{6,9,11}}
   C: \alpha=(0 3 11 13 7 10)(1 12 4 2 9 8)(5)(6)
      B_1={{1,8,10},{2,3,6},{2,5,11},{2,8,13},{2,9,12},{2,10,0},
      {3,7,13},{3,8,11},{3,10,12},{4,12,13},{5,7,12},{5,8,0},
      {6,8,12},{6,10,13}}
 # of antimorphisms of SASC-graph: 13 (fair: 1) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,12},{2,10,1},{3,7,13},{3,8,11},{3,9,1},{3,10,12},
 {4,5,10},{4,8,9},{4,11,1},{4,12,13},{5,7,12},{5,8,1},{5,9,13},{6,7,1},
 {6,8,12},{6,9,11},{6,10,13},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 3 13 6 1 2 8 12)(4 7 10 5 9 11)
      B_1={{0,5,6},{0,7,8},{0,11,12},{0,13,1},{2,5,11},{2,8,13},
      {3,7,13},{3,8,11},{4,11,1},{5,7,12},{5,8,1},{5,9,13},
      {6,7,1},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,13},{2,9,12},{2,10,3},
 {4,5,10},{4,8,9},{4,11,3},{4,12,13},{5,7,12},{5,8,3},{5,9,13},{6,7,3},
 {6,8,12},{6,9,11},{6,10,13},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,13},{8,11},{9,3},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 8 10 13)(2 9 11 4)(3 5 12 6)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{2,4,7},
      {2,5,11},{2,10,3},{4,5,10},{5,7,12},{6,7,3},{6,9,11},
      {6,10,13},{7,10,11}}
   B: \alpha=(0 7 4 13)(1 6 10 9)(2 12 3 5)(8 11)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,8,10},
      {1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,10,3},{4,5,10},
      {4,11,3},{7,10,11}}
   C: \alpha=(0 7 10 6 4 12 3 5 2 13 1 9)(8 11)
      B_1={{0,5,6},{0,7,8},{1,7,9},{1,8,10},{2,8,13},{2,9,12},
      {4,8,9},{4,12,13},{5,7,12},{5,8,3},{5,9,13},{6,7,3},
      {6,8,12},{6,10,13}}
 # of antimorphisms of SASC-graph: 38 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},{2,10,6},
 {3,7,13},{3,8,11},{3,9,6},{3,10,12},{4,5,10},{4,8,9},{4,11,6},{4,12,13},
 {5,7,12},{5,8,6},{5,9,13},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,6},{8,12},{9,11},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 4)(2 3)(5 6 7)(8 12)(9 11)(10 13)
      B_1={{0,3,4},{0,11,12},{0,13,6},{1,3,5},{1,7,9},{1,11,13},
      {1,12,6},{3,7,13},{3,8,11},{3,9,6},{3,10,12},{4,12,13},
      {5,7,12},{5,9,13}}
   B: \alpha=(0)(1 4)(2 3)(5)(6 7)(8 12)(9 11)(10 13)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,7,9},{1,8,10},{2,4,7},
      {2,5,11},{2,8,13},{2,9,12},{2,10,6},{4,5,10},{4,8,9},
      {5,7,12},{7,10,11}}
   C: \alpha=(0 5)(1 7 3 8)(2 9 13 6)(4 11 10 12)
      B_1={{1,3,5},{1,7,9},{1,12,6},{2,5,11},{2,10,6},{3,8,11},
      {3,9,6},{4,5,10},{4,8,9},{4,12,13},{5,7,12},{5,8,6},
      {5,9,13},{7,10,11}}
   D: \alpha=(0 5)(1 7 3 8)(2 12 4 6)(9 13 11 10)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},
      {1,7,9},{1,11,13},{1,12,6},{2,9,12},{3,8,11},{3,9,6},
      {3,10,12},{4,11,6}}
 # of antimorphisms of SASC-graph: 23 (fair: 7) 
 # of halving permutations: 5 (fair: 1; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=4 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,10,9},
 {3,7,13},{3,8,11},{3,10,12},{4,5,10},{4,11,9},{4,12,13},{5,7,12},{5,8,9},
 {6,7,9},{6,8,12},{6,10,13},{7,10,11}}
 I={{0,10},{1,7},{2,12},{3,9},{4,8},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 9 10 12 8)(2 3 5 7 4 13)(6 11)
      B_1={{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,11,13},{1,12,9},
      {2,4,7},{2,5,11},{2,8,13},{3,8,11},{3,10,12},{4,5,10},
      {4,11,9},{7,10,11}}
   B: \alpha=(0)(1 5 8 11)(2 12)(3 9)(4 6 7 13)(10)
      B_1={{0,1,2},{0,3,4},{0,7,8},{1,3,5},{1,4,6},{2,3,6},
      {2,4,7},{2,5,11},{2,8,13},{2,10,9},{3,7,13},{3,8,11},
      {4,5,10},{7,10,11}}
   C: \alpha=(0 1 3 13 2 9)(4 5 7 8 10 12)(6 11)
      B_1={{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,11,13},{1,12,9},
      {2,4,7},{2,5,11},{2,8,13},{3,8,11},{3,10,12},{4,5,10},
      {4,11,9},{7,10,11}}
   D: \alpha=(0 4 10 8)(1 7)(2)(3 5 9 13)(6 11)(12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{1,4,6},{1,8,10},{2,3,6},
      {2,10,9},{3,7,13},{4,12,13},{5,7,12},{5,8,9},{6,7,9},
      {6,8,12},{6,10,13}}
   E: \alpha=(0 4 5 9)(1 2 7 12)(3 10 8 13)(6 11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{1,3,5},
      {1,8,10},{1,11,13},{2,5,11},{3,7,13},{3,8,11},{5,7,12},
      {5,8,9},{7,10,11}}
 # of antimorphisms of SASC-graph: 60 (fair: 20) 
 # of halving permutations: 12 (fair: 4; strong: 2) 


 System No. 32 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,12},{2,10,0},{3,7,12},{3,8,9},{3,10,13},{3,11,0},
 {4,5,10},{4,8,0},{4,9,11},{4,12,13},{5,7,13},{5,8,12},{5,9,0},{6,7,0},
 {6,8,11},{6,9,13},{6,10,12},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 13)(1)(2 9 10)(3 4)(5 6)(7 8)(11 12)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,4,7},{2,5,11},{2,10,0},
      {3,11,0},{4,5,10},{4,8,0},{4,9,11},{5,9,0},{6,7,0},
      {6,8,11},{7,10,11}}
   B: \alpha=(0 13)(1)(2)(3 4)(5 6)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,6},{2,8,13},{2,9,12},
      {3,7,12},{3,8,9},{3,10,13},{3,11,0},{5,7,13},{5,8,12},
      {6,9,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 3 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,12},{2,10,1},{3,7,12},{3,8,9},{3,10,13},{3,11,1},
 {4,5,10},{4,8,1},{4,9,11},{4,12,13},{5,7,13},{5,8,12},{5,9,1},{6,7,1},
 {6,8,11},{6,9,13},{6,10,12},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,9},{3,10,13},{3,11,2},
 {4,5,10},{4,8,2},{4,9,11},{4,12,13},{5,7,13},{5,8,12},{5,9,2},{6,7,2},
 {6,8,11},{6,9,13},{6,10,12},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,11},{8,13},{9,12},{10,2}}
 Examples of antimorphisms:
   A: \alpha=(0 6 4 10)(1 5 9 7 11 12 3 2)(8)(13)
      B_1={{0,5,6},{0,7,8},{0,13,2},{1,12,2},{3,7,12},{4,5,10},
      {4,8,2},{4,12,13},{5,7,13},{5,8,12},{5,9,2},{6,7,2},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,13},{2,9,12},{2,10,3},
 {4,5,10},{4,8,3},{4,9,11},{4,12,13},{5,7,13},{5,8,12},{5,9,3},{6,7,3},
 {6,8,11},{6,9,13},{6,10,12},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,12},{8,9},{10,13},{11,3}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 13 4 11 2 8 3 6 10 9 7 12)
      B_1={{0,9,10},{0,11,12},{1,4,6},{1,8,10},{1,11,13},{1,12,3},
      {2,8,13},{2,9,12},{4,9,11},{5,7,13},{5,8,12},{6,7,3},
      {6,8,11},{6,9,13}}
   C: \alpha=(0 5 7 10)(1 11 9 12 3 2)(4 8 6 13)
      B_1={{0,5,6},{0,11,12},{1,11,13},{2,4,7},{2,5,11},{2,8,13},
      {2,9,12},{2,10,3},{4,5,10},{4,12,13},{5,8,12},{6,8,11},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,11},{2,8,13},{2,9,12},{2,10,4},
 {3,7,12},{3,8,9},{3,10,13},{3,11,4},{5,7,13},{5,8,12},{5,9,4},{6,7,4},
 {6,8,11},{6,9,13},{6,10,12},{7,10,11}}
 I={{0,3},{1,6},{2,7},{5,10},{8,4},{9,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,13},{2,9,12},{2,10,5},
 {3,7,12},{3,8,9},{3,10,13},{3,11,5},{4,8,5},{4,9,11},{4,12,13},{6,7,5},
 {6,8,11},{6,9,13},{6,10,12},{7,10,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,13},{8,12},{9,5}}
 Examples of antimorphisms:
   C: \alpha=(0 5 1 7)(2 6 9 8)(3 13 12 11)(4 10)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,5},{1,7,9},{1,8,10},
      {1,11,13},{2,3,6},{2,9,12},{2,10,5},{3,8,9},{3,10,13},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},{2,10,6},
 {3,7,12},{3,8,9},{3,10,13},{3,11,6},{4,5,10},{4,8,6},{4,9,11},{4,12,13},
 {5,7,13},{5,8,12},{5,9,6},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,6},{8,11},{9,13},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 5)(1 9 3 7 2 6 4 13)(8 12 11 10)
      B_1={{1,3,5},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,9,12},
      {3,8,9},{3,10,13},{4,5,10},{4,8,6},{5,7,13},{5,8,12},
      {5,9,6},{7,10,11}}
   B: \alpha=(0)(1 4)(2 3)(5)(6 7)(8 11)(9 13)(10 12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,7,9},{1,8,10},{1,11,13},
      {2,4,7},{2,5,11},{2,8,13},{2,9,12},{2,10,6},{4,5,10},
      {5,7,13},{7,10,11}}
   C: \alpha=(0 5)(1 6 3 13 2 9 4 7)(8 12 11 10)
      B_1={{1,3,5},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,9,12},
      {3,8,9},{3,10,13},{4,5,10},{4,8,6},{5,7,13},{5,8,12},
      {5,9,6},{7,10,11}}
   D: \alpha=(0 5)(1 7 2 13)(3 9 4 6)(8 11)(10)(12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},
      {1,7,9},{1,8,10},{1,12,6},{2,8,13},{2,9,12},{2,10,6},
      {3,8,9},{4,8,6}}
 # of antimorphisms of SASC-graph: 13 (fair: 7) 
 # of halving permutations: 5 (fair: 1; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,11},{2,8,13},{2,9,12},{2,10,7},
 {3,8,9},{3,10,13},{3,11,7},{4,5,10},{4,8,7},{4,9,11},{4,12,13},{5,8,12},
 {5,9,7},{6,8,11},{6,9,13},{6,10,12}}
 I={{0,8},{1,9},{2,4},{3,12},{5,13},{6,7},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,11},{2,9,12},{2,10,8},
 {3,7,12},{3,10,13},{3,11,8},{4,5,10},{4,9,11},{4,12,13},{5,7,13},{5,9,8},
 {6,7,8},{6,9,13},{6,10,12},{7,10,11}}
 I={{0,7},{1,10},{2,13},{3,9},{4,8},{5,12},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 5 8 11)(1 6 7 2)(3 13 4 9 10 12)
      B_1={{0,3,4},{0,5,6},{1,3,5},{1,4,6},{2,3,6},{2,4,7},
      {2,5,11},{2,10,8},{3,10,13},{3,11,8},{4,5,10},{4,9,11},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,10,9},
 {3,7,12},{3,10,13},{3,11,9},{4,5,10},{4,8,9},{4,12,13},{5,7,13},{5,8,12},
 {6,7,9},{6,8,11},{6,10,12},{7,10,11}}
 I={{0,10},{1,7},{2,12},{3,8},{4,11},{5,9},{6,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},
 {3,7,12},{3,8,9},{3,11,10},{4,8,10},{4,9,11},{4,12,13},{5,7,13},{5,8,12},
 {5,9,10},{6,7,10},{6,8,11},{6,9,13}}
 I={{0,9},{1,8},{2,10},{3,13},{4,5},{6,12},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 7 3 11 13 6 4 10)(1 5 2 8 12 9)
      B_1={{0,5,6},{0,7,8},{1,7,9},{2,5,11},{3,8,9},{3,11,10},
      {4,8,10},{4,9,11},{5,7,13},{5,8,12},{5,9,10},{6,7,10},
      {6,8,11},{6,9,13}}
   B: \alpha=(0 4 9 5)(1 11 10 6)(2 12 8 7)(3 13)
      B_1={{0,1,2},{0,3,4},{0,7,8},{1,3,5},{1,4,6},{2,3,6},
      {2,5,11},{2,8,13},{2,9,12},{3,8,9},{3,11,10},{4,8,10},
      {5,9,10},{6,8,11}}
   C: \alpha=(0 7 3 10)(1 5 2 8 12 9)(4 11 13 6)
      B_1={{0,5,6},{0,7,8},{1,7,9},{2,5,11},{3,8,9},{3,11,10},
      {4,8,10},{4,9,11},{5,7,13},{5,8,12},{5,9,10},{6,7,10},
      {6,8,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 8 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,8,13},{2,9,12},{2,10,11},
 {3,7,12},{3,8,9},{3,10,13},{4,5,10},{4,8,11},{4,12,13},{5,7,13},{5,8,12},
 {5,9,11},{6,7,11},{6,9,13},{6,10,12}}
 I={{0,12},{1,13},{2,5},{3,11},{4,9},{6,8},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,10,12},
 {3,8,9},{3,10,13},{3,11,12},{4,5,10},{4,8,12},{4,9,11},{5,7,13},{5,9,12},
 {6,7,12},{6,8,11},{6,9,13},{7,10,11}}
 I={{0,11},{1,12},{2,9},{3,7},{4,13},{5,8},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 10 13)(2 8 11 9 3 12)(4 7 5 6)
      B_1={{0,7,8},{0,9,10},{0,13,12},{1,4,6},{1,7,9},{1,8,10},
      {2,10,12},{3,8,9},{4,8,12},{5,7,13},{5,9,12},{6,7,12},
      {6,8,11},{6,9,13}}
   B: \alpha=(0 11)(1 7 2 13)(3 9 4 12)(5 8)(6)(10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},
      {1,4,6},{1,7,9},{1,8,10},{2,3,6},{2,8,13},{2,10,12},
      {3,8,9},{4,8,12}}
   C: \alpha=(0 2 12 6)(1 10 7 5)(3 9 4 8 11 13)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,7,9},{1,8,10},
      {1,11,13},{2,8,13},{2,10,12},{3,8,9},{4,8,12},{5,7,13},
      {5,9,12},{6,9,13}}
 # of antimorphisms of SASC-graph: 11 (fair: 3) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,11},{2,9,12},{2,10,13},
 {3,7,12},{3,8,9},{3,11,13},{4,5,10},{4,8,13},{4,9,11},{5,8,12},{5,9,13},
 {6,7,13},{6,8,11},{6,10,12},{7,10,11}}
 I={{0,13},{1,11},{2,8},{3,10},{4,12},{5,7},{6,9}}
 Examples of antimorphisms:
   B: \alpha=(0 13)(1 11)(2 8)(3 10)(4 12)(5)(6 9)(7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},
      {1,3,5},{1,7,9},{1,8,10},{2,9,12},{3,7,12},{3,8,9},
      {4,9,11},{5,8,12}}
 # of antimorphisms of SASC-graph: 1 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},
 {3,7,12},{3,8,9},{3,10,13},{4,5,10},{4,9,11},{4,12,13},{5,7,13},{5,8,12},
 {6,8,11},{6,9,13},{6,10,12},{7,10,11}}
 I={{0,13},{1,12},{2,10},{3,11},{4,8},{5,9},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 9)(2 10)(4 7 11 5)(6 13 12 8)
      B_1={{0,1,2},{0,3,4},{0,11,12},{1,4,6},{1,11,13},{2,3,6},
      {2,4,7},{2,5,11},{2,8,13},{2,9,12},{3,8,9},{4,9,11},
      {4,12,13},{6,8,11}}
   C: \alpha=(0 1 8 6)(2 10)(3 9 13 12)(4 7 11 5)
      B_1={{0,1,2},{0,3,4},{0,11,12},{1,4,6},{1,11,13},{2,3,6},
      {2,4,7},{2,5,11},{2,8,13},{2,9,12},{3,8,9},{4,9,11},
      {4,12,13},{6,8,11}}
 # of antimorphisms of SASC-graph: 10 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 33 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,0},{2,10,12},{3,7,12},{3,8,9},{3,10,13},{3,11,0},
 {4,5,10},{4,8,0},{4,9,11},{4,12,13},{5,7,0},{5,8,12},{5,9,13},{6,7,13},
 {6,8,11},{6,9,12},{6,10,0},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,1},{2,10,12},{3,7,12},{3,8,9},{3,10,13},{3,11,1},
 {4,5,10},{4,8,1},{4,9,11},{4,12,13},{5,7,1},{5,8,12},{5,9,13},{6,7,13},
 {6,8,11},{6,9,12},{6,10,1},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,12},{3,8,9},{3,10,13},{3,11,2},
 {4,5,10},{4,8,2},{4,9,11},{4,12,13},{5,7,2},{5,8,12},{5,9,13},{6,7,13},
 {6,8,11},{6,9,12},{6,10,2},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,11},{8,13},{9,2},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,13},{2,9,3},{2,10,12},
 {4,5,10},{4,8,3},{4,9,11},{4,12,13},{5,7,3},{5,8,12},{5,9,13},{6,7,13},
 {6,8,11},{6,9,12},{6,10,3},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,12},{8,9},{10,13},{11,3}}
 Examples of antimorphisms:
   A: \alpha=(0 9 2 11)(1 10 3 4)(5 13 8 6)(7 12)
      B_1={{0,7,8},{0,9,10},{1,7,9},{1,8,10},{2,4,7},{2,5,11},
      {4,5,10},{4,8,3},{4,9,11},{5,7,3},{5,9,13},{6,7,13},
      {6,8,11},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,11},{2,8,13},{2,9,4},{2,10,12},
 {3,7,12},{3,8,9},{3,10,13},{3,11,4},{5,7,4},{5,8,12},{5,9,13},{6,7,13},
 {6,8,11},{6,9,12},{6,10,4},{7,10,11}}
 I={{0,3},{1,6},{2,7},{5,10},{8,4},{9,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,13},{2,9,5},{2,10,12},
 {3,7,12},{3,8,9},{3,10,13},{3,11,5},{4,8,5},{4,9,11},{4,12,13},{6,7,13},
 {6,8,11},{6,9,12},{6,10,5},{7,10,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,5},{8,12},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,13},{2,9,6},{2,10,12},
 {3,7,12},{3,8,9},{3,10,13},{3,11,6},{4,5,10},{4,8,6},{4,9,11},{4,12,13},
 {5,7,6},{5,8,12},{5,9,13},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,13},{8,11},{9,12},{10,6}}
 Examples of antimorphisms:
   A: \alpha=(0 1 10 13)(2 12 7 5)(3 9 4 6)(8 11)
      B_1={{0,1,2},{0,3,4},{0,11,12},{1,3,5},{1,11,13},{2,4,7},
      {2,5,11},{3,7,12},{3,8,9},{3,10,13},{4,5,10},{4,8,6},
      {4,12,13},{7,10,11}}
   C: \alpha=(0 2 10 7)(1 12 13 5)(3 6 4 9)(8 11)
      B_1={{0,1,2},{0,3,4},{0,11,12},{1,3,5},{1,11,13},{2,4,7},
      {2,5,11},{3,7,12},{3,8,9},{3,10,13},{4,5,10},{4,8,6},
      {4,12,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,11},{2,8,13},{2,9,7},{2,10,12},
 {3,8,9},{3,10,13},{3,11,7},{4,5,10},{4,8,7},{4,9,11},{4,12,13},{5,8,12},
 {5,9,13},{6,8,11},{6,9,12},{6,10,7}}
 I={{0,8},{1,9},{2,4},{3,12},{5,7},{6,13},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,11},{2,9,8},{2,10,12},
 {3,7,12},{3,10,13},{3,11,8},{4,5,10},{4,9,11},{4,12,13},{5,7,8},{5,9,13},
 {6,7,13},{6,9,12},{6,10,8},{7,10,11}}
 I={{0,7},{1,10},{2,13},{3,9},{4,8},{5,12},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 6 10 3)(2 12 9 4)(7 11 8 13)
      B_1={{0,3,4},{1,3,5},{1,4,6},{1,7,9},{1,11,13},{1,12,8},
      {2,3,6},{2,4,7},{2,9,8},{3,7,12},{3,11,8},{6,7,13},
      {6,9,12},{6,10,8}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,10,12},
 {3,7,12},{3,10,13},{3,11,9},{4,5,10},{4,8,9},{4,12,13},{5,7,9},{5,8,12},
 {6,7,13},{6,8,11},{6,10,9},{7,10,11}}
 I={{0,10},{1,7},{2,9},{3,8},{4,11},{5,13},{6,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,9,10},
 {3,7,12},{3,8,9},{3,11,10},{4,8,10},{4,9,11},{4,12,13},{5,7,10},{5,8,12},
 {5,9,13},{6,7,13},{6,8,11},{6,9,12}}
 I={{0,9},{1,8},{2,12},{3,13},{4,5},{6,10},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 8 13 6 5 1 7 11 10 4 3 9)(2 12)
      B_1={{0,3,4},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,12,10},
      {3,7,12},{3,11,10},{4,12,13},{5,7,10},{5,8,12},{5,9,13},
      {6,7,13},{6,9,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,8,13},{2,9,11},{2,10,12},
 {3,7,12},{3,8,9},{3,10,13},{4,5,10},{4,8,11},{4,12,13},{5,7,11},{5,8,12},
 {5,9,13},{6,7,13},{6,9,12},{6,10,11}}
 I={{0,12},{1,13},{2,5},{3,11},{4,9},{6,8},{7,10}}
 Examples of antimorphisms:
   C: \alpha=(0 1 9 6)(2 7 12 5 3 8)(4 10 11 13)
      B_1={{0,1,2},{0,3,4},{1,3,5},{1,4,6},{1,12,11},{2,3,6},
      {2,8,13},{2,9,11},{2,10,12},{3,7,12},{3,10,13},{4,12,13},
      {6,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},
 {3,8,9},{3,10,13},{3,11,12},{4,5,10},{4,8,12},{4,9,11},{5,7,12},{5,9,13},
 {6,7,13},{6,8,11},{6,10,12},{7,10,11}}
 I={{0,11},{1,12},{2,10},{3,7},{4,13},{5,8},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0 2 4 6 5 11 9 3 10 12)(1 7 8 13)
      B_1={{0,1,2},{0,7,8},{1,3,5},{1,4,6},{1,8,10},{1,11,13},
      {2,3,6},{2,5,11},{2,9,12},{3,8,9},{3,11,12},{4,8,12},
      {6,8,11},{6,10,12}}
   B: \alpha=(0 3 13 8)(1)(2 10)(4 5 11 7)(6 9)(12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,13,12},{1,4,6},{1,11,13},
      {2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},{5,7,12},
      {6,7,13},{6,8,11}}
   C: \alpha=(0 2 4 12)(1 7 8 13)(3 10 6 5 11 9)
      B_1={{0,7,8},{0,13,12},{1,3,5},{1,4,6},{1,8,10},{1,11,13},
      {2,3,6},{2,4,7},{2,5,11},{2,9,12},{3,8,9},{3,11,12},
      {6,8,11},{6,10,12}}
 # of antimorphisms of SASC-graph: 15 (fair: 3) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,11},{2,9,13},{2,10,12},
 {3,7,12},{3,8,9},{3,11,13},{4,5,10},{4,8,13},{4,9,11},{5,7,13},{5,8,12},
 {6,8,11},{6,9,12},{6,10,13},{7,10,11}}
 I={{0,13},{1,11},{2,8},{3,10},{4,12},{5,9},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 3 8 12)(1 13 2 11 4 10)(5 9)(6 7)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {2,3,6},{2,4,7},{2,9,13},{3,7,12},{3,8,9},{4,8,13},
      {4,9,11},{6,9,12}}
   C: \alpha=(0)(1 11)(2 5 3 12)(4 9 7 10 8 6)(13)
      B_1={{0,5,6},{0,9,10},{0,11,12},{2,5,11},{2,9,13},{3,7,12},
      {3,11,13},{4,5,10},{4,9,11},{5,8,12},{6,8,11},{6,9,12},
      {6,10,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,10,12},
 {3,7,12},{3,8,9},{3,10,13},{4,5,10},{4,9,11},{4,12,13},{5,8,12},{5,9,13},
 {6,7,13},{6,8,11},{6,9,12},{7,10,11}}
 I={{0,13},{1,12},{2,9},{3,11},{4,8},{5,7},{6,10}}
 Examples of antimorphisms:
   B: \alpha=(0 13)(1 12)(2 4 9 8)(3 11)(5 7)(6)(10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},
      {1,7,9},{2,3,6},{2,4,7},{2,10,12},{3,7,12},{3,8,9},
      {6,9,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 34 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,0},{2,10,12},{3,7,13},{3,8,11},{3,9,12},{3,10,0},
 {4,5,10},{4,8,0},{4,9,11},{4,12,13},{5,7,0},{5,8,12},{5,9,13},{6,7,12},
 {6,8,9},{6,11,0},{6,10,13},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 2 12 3)(1 5 8 13)(4 6 7 11)(9 10)
      B_1={{1,7,9},{1,11,13},{1,12,0},{2,10,12},{3,10,0},{4,8,0},
      {4,9,11},{4,12,13},{5,7,0},{5,8,12},{5,9,13},{6,7,12},
      {6,8,9},{6,11,0}}
   C: \alpha=(0 2 12 3)(1 6 7 13)(4 5 8 11)(9 10)
      B_1={{1,11,13},{1,12,0},{2,10,12},{3,10,0},{4,8,0},{4,9,11},
      {4,12,13},{5,7,0},{5,8,12},{5,9,13},{6,7,12},{6,8,9},
      {6,11,0},{6,10,13}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,11},{2,8,13},{2,9,1},{2,10,12},{3,7,13},{3,8,11},{3,9,12},{3,10,1},
 {4,5,10},{4,8,1},{4,9,11},{4,12,13},{5,7,1},{5,8,12},{5,9,13},{6,7,12},
 {6,8,9},{6,11,1},{6,10,13},{7,10,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,7,13},{3,8,11},{3,9,12},{3,10,2},
 {4,5,10},{4,8,2},{4,9,11},{4,12,13},{5,7,2},{5,8,12},{5,9,13},{6,7,12},
 {6,8,9},{6,11,2},{6,10,13},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,11},{8,13},{9,2},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,7},{2,5,11},{2,8,13},{2,9,3},{2,10,12},
 {4,5,10},{4,8,3},{4,9,11},{4,12,13},{5,7,3},{5,8,12},{5,9,13},{6,7,12},
 {6,8,9},{6,11,3},{6,10,13},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,13},{8,11},{9,12},{10,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,6},{2,5,11},{2,8,13},{2,9,4},{2,10,12},
 {3,7,13},{3,8,11},{3,9,12},{3,10,4},{5,7,4},{5,8,12},{5,9,13},{6,7,12},
 {6,8,9},{6,11,4},{6,10,13},{7,10,11}}
 I={{0,3},{1,6},{2,7},{5,10},{8,4},{9,11},{12,13}}
 Examples of antimorphisms:
   C: \alpha=(0 4 6 3 1 8)(2 12 9 7 13 11)(5 10)
      B_1={{0,5,6},{0,7,8},{1,3,5},{1,12,4},{2,5,11},{2,8,13},
      {2,9,4},{3,7,13},{3,8,11},{3,9,12},{5,7,4},{5,8,12},
      {5,9,13},{6,11,4}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,6},{2,4,7},{2,8,13},{2,9,5},{2,10,12},
 {3,7,13},{3,8,11},{3,9,12},{3,10,5},{4,8,5},{4,9,11},{4,12,13},{6,7,12},
 {6,8,9},{6,11,5},{6,10,13},{7,10,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,5},{8,12},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,4,7},{2,5,11},{2,8,13},{2,9,6},{2,10,12},
 {3,7,13},{3,8,11},{3,9,12},{3,10,6},{4,5,10},{4,8,6},{4,9,11},{4,12,13},
 {5,7,6},{5,8,12},{5,9,13},{7,10,11}}
 I={{0,5},{1,4},{2,3},{7,12},{8,9},{11,6},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 4 6 10)(1 11 2 9)(3 8 13 5)(7 12)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,6},{1,3,5},{1,11,13},
      {1,12,6},{2,8,13},{2,9,6},{2,10,12},{3,7,13},{3,9,12},
      {3,10,6},{4,12,13}}
   C: \alpha=(0 4 6 10 1 11 2 9)(3 8 13 5)(7 12)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,6},{1,3,5},{1,11,13},
      {1,12,6},{2,8,13},{2,9,6},{2,10,12},{3,7,13},{3,9,12},
      {3,10,6},{4,12,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,3,6},{2,5,11},{2,8,13},{2,9,7},{2,10,12},
 {3,8,11},{3,9,12},{3,10,7},{4,5,10},{4,8,7},{4,9,11},{4,12,13},{5,8,12},
 {5,9,13},{6,8,9},{6,11,7},{6,10,13}}
 I={{0,8},{1,9},{2,4},{3,13},{5,7},{6,12},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,6},{2,4,7},{2,5,11},{2,9,8},{2,10,12},
 {3,7,13},{3,9,12},{3,10,8},{4,5,10},{4,9,11},{4,12,13},{5,7,8},{5,9,13},
 {6,7,12},{6,11,8},{6,10,13},{7,10,11}}
 I={{0,7},{1,10},{2,13},{3,11},{4,8},{5,12},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0 2 12 7 13 5)(1 10)(3 9 6)(4 8)(11)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
      {1,7,9},{1,11,13},{1,12,8},{2,3,6},{4,9,11},{4,12,13},
      {5,9,13},{6,7,12}}
   B: \alpha=(0 5 13 10)(1 7 12 2)(3)(4 8)(6 9)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,8},{1,4,6},
      {1,11,13},{1,12,8},{2,3,6},{3,7,13},{4,9,11},{4,12,13},
      {6,7,12},{6,10,13}}
   C: \alpha=(0 1 3 8)(2 13)(4 7 9 12)(5 10 11 6)
      B_1={{0,11,12},{0,13,8},{1,3,5},{1,7,9},{1,11,13},{1,12,8},
      {3,7,13},{4,5,10},{4,9,11},{4,12,13},{5,7,8},{5,9,13},
      {6,11,8},{6,10,13}}
   D: \alpha=(0 10 13 5)(1 2 12 7)(3)(4 8)(6 9)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,8},{1,4,6},
      {1,11,13},{1,12,8},{2,3,6},{3,7,13},{4,9,11},{4,12,13},
      {6,7,12},{6,10,13}}
 # of antimorphisms of SASC-graph: 14 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,10,12},
 {3,7,13},{3,8,11},{3,10,9},{4,5,10},{4,8,9},{4,12,13},{5,7,9},{5,8,12},
 {6,7,12},{6,11,9},{6,10,13},{7,10,11}}
 I={{0,10},{1,7},{2,9},{3,12},{4,11},{5,13},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,9,10},
 {3,7,13},{3,8,11},{3,9,12},{4,8,10},{4,9,11},{4,12,13},{5,7,10},{5,8,12},
 {5,9,13},{6,7,12},{6,8,9},{6,11,10}}
 I={{0,9},{1,8},{2,12},{3,10},{4,5},{6,13},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 6 2 11)(1 5 13 8 3 9)(4 10 12 7)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
      {1,11,13},{1,12,10},{2,3,6},{2,4,7},{2,8,13},{3,7,13},
      {3,9,12},{4,12,13}}
 # of antimorphisms of SASC-graph: 10 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,6},{2,4,7},{2,8,13},{2,9,11},{2,10,12},
 {3,7,13},{3,9,12},{3,10,11},{4,5,10},{4,8,11},{4,12,13},{5,7,11},{5,8,12},
 {5,9,13},{6,7,12},{6,8,9},{6,10,13}}
 I={{0,12},{1,13},{2,5},{3,8},{4,9},{6,11},{7,10}}
 Examples of antimorphisms:
   B: \alpha=(0 5 13 10)(1 7 12 2)(3)(4 9)(6 11)(8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,4,6},{2,3,6},
      {2,4,7},{2,8,13},{3,7,13},{4,5,10},{4,8,11},{4,12,13},
      {6,7,12},{6,10,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,9,12},
 {3,7,13},{3,8,11},{3,10,12},{4,5,10},{4,8,12},{4,9,11},{5,7,12},{5,9,13},
 {6,8,9},{6,11,12},{6,10,13},{7,10,11}}
 I={{0,11},{1,12},{2,10},{3,9},{4,13},{5,8},{6,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,6},{2,4,7},{2,5,11},{2,9,13},{2,10,12},
 {3,8,11},{3,9,12},{3,10,13},{4,5,10},{4,8,13},{4,9,11},{5,7,13},{5,8,12},
 {6,7,12},{6,8,9},{6,11,13},{7,10,11}}
 I={{0,13},{1,11},{2,8},{3,7},{4,12},{5,9},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 12 7)(2 10 4 3)(5 13 6 9 11 8)
      B_1={{0,1,2},{0,5,6},{0,11,12},{1,3,5},{1,4,6},{2,3,6},
      {2,4,7},{2,5,11},{4,5,10},{4,9,11},{5,8,12},{6,7,12},
      {6,11,13},{7,10,11}}
   C: \alpha=(0 3 7 12 11 1 2 6)(4 8 9 10 13 5)
      B_1={{0,1,2},{0,5,6},{0,7,8},{1,3,5},{1,8,10},{2,5,11},
      {2,10,12},{3,8,11},{3,10,13},{4,5,10},{5,8,12},{6,7,12},
      {6,8,9},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,6},{2,4,7},{2,5,11},{2,8,13},{2,10,12},
 {3,7,13},{3,8,11},{3,9,12},{4,5,10},{4,9,11},{4,12,13},{5,8,12},{5,9,13},
 {6,7,12},{6,8,9},{6,10,13},{7,10,11}}
 I={{0,13},{1,12},{2,9},{3,10},{4,8},{5,7},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 35 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=3 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,12},{2,9,13},{2,10,0},{3,6,13},{3,8,11},{3,9,0},{3,10,12},
 {4,5,0},{4,7,13},{4,9,12},{4,10,11},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,0},{6,9,11},{7,11,0},{8,12,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=3 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,12},{2,9,13},{2,10,1},{3,6,13},{3,8,11},{3,9,1},{3,10,12},
 {4,5,1},{4,7,13},{4,9,12},{4,10,11},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,1},{6,9,11},{7,11,1},{8,12,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 2)(1 4 10 3 13 8)(5 11 12 6)(7 9)
      B_1={{0,9,10},{0,13,1},{2,5,11},{2,6,12},{2,9,13},{2,10,1},
      {3,9,1},{3,10,12},{4,5,1},{4,9,12},{5,8,9},{5,10,13},
      {6,9,11},{8,12,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=3 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,13},{3,8,11},{3,9,2},{3,10,12},
 {4,5,2},{4,7,13},{4,9,12},{4,10,11},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,2},{6,9,11},{7,11,2},{8,12,13}}
 I={{0,1},{3,7},{4,8},{5,11},{6,12},{9,13},{10,2}}
 Examples of antimorphisms:
   B: \alpha=(0 2 1 10)(3 4 13 12)(5 11)(6 7 8 9)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{1,4,6},{1,7,9},
      {1,11,13},{1,12,2},{3,6,13},{3,8,11},{4,10,11},{6,9,11},
      {7,11,2},{8,12,13}}
   D: \alpha=(0 4 1 8)(2 3 6 5)(7 12 11 10)(9 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,7,9},
      {1,8,10},{1,12,2},{3,9,2},{4,9,12},{5,8,9},{6,7,10},
      {6,9,11},{7,11,2}}
 # of antimorphisms of SASC-graph: 6 (fair: 6) 
 # of halving permutations: 3 (fair: 3; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,12},{2,9,13},{2,10,3},
 {4,5,3},{4,7,13},{4,9,12},{4,10,11},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,3},{6,9,11},{7,11,3},{8,12,13}}
 I={{0,4},{1,5},{2,7},{6,13},{8,11},{9,3},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,12},{2,9,13},{2,10,4},
 {3,6,13},{3,8,11},{3,9,4},{3,10,12},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,4},{6,9,11},{7,11,4},{8,12,13}}
 I={{0,3},{1,6},{2,8},{5,4},{7,13},{9,12},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 3)(1 6)(2 10 7 8 11 13)(4 12 9)(5)
      B_1={{1,3,5},{2,3,7},{2,5,11},{2,6,12},{2,9,13},{3,6,13},
      {3,8,11},{3,9,4},{3,10,12},{5,7,12},{6,7,10},{6,8,4},
      {6,9,11},{7,11,4}}
   B: \alpha=(0 3)(1 4 6 5)(2 8)(7 13)(9 12)(10)(11)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},
      {1,12,4},{2,5,11},{2,6,12},{2,10,4},{5,7,12},{5,10,13},
      {7,11,4},{8,12,13}}
   C: \alpha=(0 8 12 3 2 9)(1 5 6 4)(7 13 10)(11)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,11,12},{0,13,4},{1,12,4},
      {2,5,11},{2,6,12},{2,9,13},{2,10,4},{3,10,12},{5,7,12},
      {5,10,13},{7,11,4}}
 # of antimorphisms of SASC-graph: 8 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,12},{2,9,13},{2,10,5},
 {3,6,13},{3,8,11},{3,9,5},{3,10,12},{4,7,13},{4,9,12},{4,10,11},{6,7,10},
 {6,8,5},{6,9,11},{7,11,5},{8,12,13}}
 I={{0,6},{1,3},{2,11},{4,5},{7,12},{8,9},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,8},{2,5,11},{2,9,13},{2,10,6},
 {3,8,11},{3,9,6},{3,10,12},{4,5,6},{4,7,13},{4,9,12},{4,10,11},{5,7,12},
 {5,8,9},{5,10,13},{7,11,6},{8,12,13}}
 I={{0,5},{1,4},{2,12},{3,13},{7,10},{8,6},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 36 
 |Aut(S)|=4 


 Subsystem No. 0 
 |Aut(T)|=4 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,12},{2,9,0},{2,10,13},{3,6,13},{3,8,11},{3,9,12},{3,10,0},
 {4,5,0},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{6,7,10},
 {6,8,0},{6,9,11},{7,11,0},{8,12,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 1 13 7 2 8)(3 4 5 12 11 6)(9 10)
      B_1={{1,4,6},{1,7,9},{1,11,13},{2,3,7},{2,6,12},{2,9,0},
      {3,9,12},{4,5,0},{4,7,12},{4,9,13},{5,8,9},{6,8,0},
      {6,9,11},{8,12,13}}
   B: \alpha=(0)(1 2)(3 4)(5 6)(7 8)(9 10)(11 12)(13)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,7},{2,5,11},{2,9,0},
      {3,8,11},{3,9,12},{4,5,0},{4,9,13},{5,7,13},{5,8,9},
      {5,10,12},{7,11,0}}
   C: \alpha=(0 1 13 7 2 8)(3 4)(5 9 10 6 12 11)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,7},{2,5,11},{2,9,0},
      {3,6,13},{3,8,11},{3,9,12},{3,10,0},{5,10,12},{6,7,10},
      {6,8,0},{8,12,13}}
   D: \alpha=(0)(1 2)(3 4)(5 8 11 10)(6 7 12 9)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,8,11},{3,10,0},{4,7,12},{4,9,13},{5,7,13},{5,10,12},
      {6,8,0},{6,9,11}}
   E: \alpha=(0 3 13 4)(1 2)(5 10 6 9)(7 11 8 12)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,6,13},{3,8,11},{3,9,12},{4,5,0},{4,7,12},{4,10,11},
      {5,8,9},{6,7,10}}
 # of antimorphisms of SASC-graph: 85 (fair: 49) 
 # of halving permutations: 13 (fair: 9; strong: 3) 


 Subsystem No. 1 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,12},{2,9,1},{2,10,13},{3,6,13},{3,8,11},{3,9,12},{3,10,1},
 {4,5,1},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{6,7,10},
 {6,8,1},{6,9,11},{7,11,1},{8,12,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,12},{2,9,3},{2,10,13},
 {4,5,3},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{6,7,10},
 {6,8,3},{6,9,11},{7,11,3},{8,12,13}}
 I={{0,4},{1,5},{2,7},{6,13},{8,11},{9,12},{10,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,12},{2,9,5},{2,10,13},
 {3,6,13},{3,8,11},{3,9,12},{3,10,5},{4,7,12},{4,9,13},{4,10,11},{6,7,10},
 {6,8,5},{6,9,11},{7,11,5},{8,12,13}}
 I={{0,6},{1,3},{2,11},{4,5},{7,13},{8,9},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,12},{2,9,7},{2,10,13},
 {3,6,13},{3,8,11},{3,9,12},{3,10,7},{4,5,7},{4,9,13},{4,10,11},{5,8,9},
 {5,10,12},{6,8,7},{6,9,11},{8,12,13}}
 I={{0,8},{1,9},{2,3},{4,12},{5,13},{6,10},{11,7}}
 Examples of antimorphisms:
   A: \alpha=(0 9 12 8 3 13)(1 2 7 10)(4 11 6 5)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,7},{1,3,5},
      {1,12,7},{2,5,11},{2,6,12},{3,8,11},{3,9,12},{3,10,7},
      {4,10,11},{5,10,12}}
   B: \alpha=(0 6 8 10)(1 13 4 7)(2)(3)(5 12 11 9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,8,10},{1,11,13},{2,4,8},{2,5,11},{3,8,11},{4,5,7},
      {4,10,11},{5,8,9}}
   C: \alpha=(0 2 5 4)(1 6 8 3)(7 11)(9 10 13 12)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,8,10},
      {1,12,7},{2,5,11},{2,6,12},{3,10,7},{4,10,11},{5,10,12},
      {6,8,7},{8,12,13}}
   D: \alpha=(0 10 8 6)(1 7 4 13)(2 3)(5 9 11 12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,8,10},{1,11,13},{2,4,8},{2,5,11},{3,8,11},{4,5,7},
      {4,10,11},{5,8,9}}
 # of antimorphisms of SASC-graph: 8 (fair: 4) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 System No. 37 
 |Aut(S)|=12 


 Subsystem No. 0 
 |Aut(T)|=12 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,12},{2,9,0},{2,10,13},{3,6,9},{3,8,13},{3,10,12},{3,11,0},
 {4,5,10},{4,7,0},{4,9,11},{4,12,13},{5,7,12},{5,8,0},{5,9,13},{6,7,13},
 {6,8,11},{6,10,0},{7,10,11},{8,9,12}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 1 13)(2)(3 8 7 4 9 10)(5 6)(11 12)
      B_1={{1,3,5},{1,8,10},{1,12,0},{2,4,8},{2,5,11},{2,10,13},
      {3,10,12},{4,5,10},{4,7,0},{4,12,13},{5,7,12},{5,8,0},
      {5,9,13},{8,9,12}}
   B: \alpha=(0)(1 2)(3 4)(5 6)(7 8)(9 10)(11 12)(13)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,7},{2,5,11},{2,9,0},
      {3,6,9},{3,8,13},{3,10,12},{3,11,0},{5,7,12},{5,8,0},
      {5,9,13},{7,10,11}}
   D: \alpha=(0)(1 2)(3 6 11 10)(4 5 12 9)(7 8)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,8,13},{3,10,12},{3,11,0},{4,7,0},{4,9,11},{4,12,13},
      {5,7,12},{6,8,11}}
   E: \alpha=(0 3 13 4)(1 2)(5 10 6 9)(7 11 8 12)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,6,9},{3,8,13},{3,10,12},{4,5,10},{4,7,0},{4,9,11},
      {5,7,12},{6,8,11}}
 # of antimorphisms of SASC-graph: 201 (fair: 165) 
 # of halving permutations: 27 (fair: 27; strong: 9) 


 Subsystem No. 1 
 |Aut(T)|=6 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,12},{2,9,1},{2,10,13},{3,6,9},{3,8,13},{3,10,12},{3,11,1},
 {4,5,10},{4,7,1},{4,9,11},{4,12,13},{5,7,12},{5,8,1},{5,9,13},{6,7,13},
 {6,8,11},{6,10,1},{7,10,11},{8,9,12}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,12},{2,9,3},{2,10,13},
 {4,5,10},{4,7,3},{4,9,11},{4,12,13},{5,7,12},{5,8,3},{5,9,13},{6,7,13},
 {6,8,11},{6,10,3},{7,10,11},{8,9,12}}
 I={{0,4},{1,5},{2,7},{6,9},{8,13},{10,12},{11,3}}
 Examples of antimorphisms:
   A: \alpha=(0 10 1 11)(2)(3 12 9 5 4 6)(7)(8 13)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,7,9},{1,8,10},{2,4,8},
      {2,9,3},{4,5,10},{4,7,3},{4,9,11},{5,8,3},{6,8,11},
      {6,10,3},{8,9,12}}
   C: \alpha=(0 10 1 11)(2 7)(3 12 9 5 4 6)(8 13)
      B_1={{0,7,8},{0,11,12},{1,7,9},{1,8,10},{2,4,8},{2,9,3},
      {4,5,10},{4,7,3},{4,9,11},{5,8,3},{6,8,11},{6,10,3},
      {7,10,11},{8,9,12}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 38 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,12},{2,10,0},{3,6,9},{3,8,12},{3,10,13},{3,11,0},
 {4,5,12},{4,7,0},{4,9,13},{4,10,11},{5,7,10},{5,8,13},{5,9,0},{6,7,11},
 {6,8,0},{6,10,12},{7,12,13},{8,9,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   C: \alpha=(0 13)(1 6 7 12)(2 4 11 8 3 5)(9 10)
      B_1={{1,4,6},{1,8,10},{1,11,13},{2,3,7},{2,5,11},{2,6,13},
      {2,10,0},{3,8,12},{3,10,13},{3,11,0},{4,10,11},{5,7,10},
      {6,10,12},{7,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,12},{2,10,1},{3,6,9},{3,8,12},{3,10,13},{3,11,1},
 {4,5,12},{4,7,1},{4,9,13},{4,10,11},{5,7,10},{5,8,13},{5,9,1},{6,7,11},
 {6,8,1},{6,10,12},{7,12,13},{8,9,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 5 7 2 6 10)(1 4 8 11)(3 13 12 9)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,1},{2,3,7},
      {3,6,9},{4,7,1},{4,9,13},{6,7,11},{6,8,1},{6,10,12},
      {7,12,13},{8,9,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,12},{3,10,13},{3,11,2},
 {4,5,12},{4,7,2},{4,9,13},{4,10,11},{5,7,10},{5,8,13},{5,9,2},{6,7,11},
 {6,8,2},{6,10,12},{7,12,13},{8,9,11}}
 I={{0,1},{3,7},{4,8},{5,11},{6,13},{9,12},{10,2}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 4 13 3 12 6)(5 11)(7 9 10 8)
      B_1={{0,11,12},{0,13,2},{1,7,9},{1,8,10},{1,11,13},{1,12,2},
      {3,10,13},{3,11,2},{4,7,2},{4,10,11},{6,7,11},{6,10,12},
      {7,12,13},{8,9,11}}
   C: \alpha=(0 1)(2 12 11 13)(3 7)(4 9 5 8 6 10)
      B_1={{0,3,4},{0,5,6},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
      {3,6,9},{3,8,12},{3,10,13},{3,11,2},{4,5,12},{4,9,13},
      {5,8,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,13},{2,9,12},{2,10,3},
 {4,5,12},{4,7,3},{4,9,13},{4,10,11},{5,7,10},{5,8,13},{5,9,3},{6,7,11},
 {6,8,3},{6,10,12},{7,12,13},{8,9,11}}
 I={{0,4},{1,5},{2,7},{6,9},{8,12},{10,13},{11,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{2,10,4},
 {3,6,9},{3,8,12},{3,10,13},{3,11,4},{5,7,10},{5,8,13},{5,9,4},{6,7,11},
 {6,8,4},{6,10,12},{7,12,13},{8,9,11}}
 I={{0,3},{1,6},{2,8},{5,12},{7,4},{9,13},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,10,5},
 {3,6,9},{3,8,12},{3,10,13},{3,11,5},{4,7,5},{4,9,13},{4,10,11},{6,7,11},
 {6,8,5},{6,10,12},{7,12,13},{8,9,11}}
 I={{0,6},{1,3},{2,11},{4,12},{7,10},{8,13},{9,5}}
 Examples of antimorphisms:
   A: \alpha=(0 8 6 13 4 10 9 11)(1)(2 12 7 5)(3)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{1,4,6},{1,7,9},
      {2,3,7},{2,4,8},{2,10,5},{3,6,9},{4,9,13},{6,7,11},
      {6,8,5},{7,12,13}}
   C: \alpha=(0 3 10 11 2 12 1 8 9 5)(4 7 6 13)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,13,5},{1,7,9},{1,8,10},
      {1,11,13},{2,3,7},{2,9,12},{2,10,5},{3,10,13},{4,9,13},
      {6,7,11},{7,12,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,6},
 {3,8,12},{3,10,13},{3,11,6},{4,5,12},{4,7,6},{4,9,13},{4,10,11},{5,7,10},
 {5,8,13},{5,9,6},{7,12,13},{8,9,11}}
 I={{0,5},{1,4},{2,13},{3,9},{7,11},{8,6},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},{2,10,7},
 {3,6,9},{3,8,12},{3,10,13},{3,11,7},{4,5,12},{4,9,13},{4,10,11},{5,8,13},
 {5,9,7},{6,8,7},{6,10,12},{8,9,11}}
 I={{0,8},{1,9},{2,3},{4,7},{5,10},{6,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{2,10,8},
 {3,6,9},{3,10,13},{3,11,8},{4,5,12},{4,7,8},{4,9,13},{4,10,11},{5,7,10},
 {5,9,8},{6,7,11},{6,10,12},{7,12,13}}
 I={{0,7},{1,10},{2,4},{3,12},{5,13},{6,8},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,9},
 {3,8,12},{3,10,13},{3,11,9},{4,5,12},{4,7,9},{4,10,11},{5,7,10},{5,8,13},
 {6,7,11},{6,8,9},{6,10,12},{7,12,13}}
 I={{0,10},{1,7},{2,12},{3,6},{4,13},{5,9},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,9},{3,8,12},{3,11,10},{4,5,12},{4,7,10},{4,9,13},{5,8,13},{5,9,10},
 {6,7,11},{6,8,10},{7,12,13},{8,9,11}}
 I={{0,9},{1,8},{2,10},{3,13},{4,11},{5,7},{6,12}}
 Examples of antimorphisms:
   A: \alpha=(0 3 1 9 13 8)(2 6 10 12)(4 5 7)(11)
      B_1={{0,7,8},{1,3,5},{2,3,7},{2,4,8},{2,5,11},{2,9,12},
      {3,6,9},{3,8,12},{3,11,10},{4,7,10},{4,9,13},{5,9,10},
      {6,8,10},{8,9,11}}
   B: \alpha=(0 9)(1 8)(2 6 10 12)(3 13)(4)(5 7)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},
      {1,4,6},{1,11,13},{1,12,10},{2,6,13},{4,5,12},{5,8,13},
      {6,7,11},{7,12,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,10,11},
 {3,6,9},{3,8,12},{3,10,13},{4,5,12},{4,7,11},{4,9,13},{5,7,10},{5,8,13},
 {5,9,11},{6,8,11},{6,10,12},{7,12,13}}
 I={{0,12},{1,13},{2,5},{3,11},{4,10},{6,7},{8,9}}
 Examples of antimorphisms:
   C: \alpha=(0 2 11 8)(1 10 9 12)(3 13 4 5)(6 7)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
      {1,7,9},{1,12,11},{2,6,13},{3,6,9},{4,9,13},{5,8,13},
      {5,9,11},{6,8,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,12},
 {3,6,9},{3,10,13},{3,11,12},{4,7,12},{4,9,13},{4,10,11},{5,7,10},{5,8,13},
 {5,9,12},{6,7,11},{6,8,12},{8,9,11}}
 I={{0,11},{1,12},{2,9},{3,8},{4,5},{6,10},{7,13}}
 Examples of antimorphisms:
   A: \alpha=(0 6 3 8 1 11 4 9 2 7)(5 12 10 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,3,5},{1,4,6},
      {1,8,10},{2,3,7},{2,4,8},{2,5,11},{3,10,13},{4,10,11},
      {5,7,10},{5,9,12}}
   C: \alpha=(0 6 4 11 7 12)(1 10 13 5)(2 9)(3 8)
      B_1={{0,9,10},{0,13,12},{1,4,6},{1,7,9},{1,8,10},{1,11,13},
      {3,6,9},{3,11,12},{4,9,13},{5,8,13},{5,9,12},{6,7,11},
      {6,8,12},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,13},
 {3,6,9},{3,8,12},{3,11,13},{4,5,12},{4,7,13},{4,10,11},{5,7,10},{5,9,13},
 {6,7,11},{6,8,13},{6,10,12},{8,9,11}}
 I={{0,13},{1,11},{2,6},{3,10},{4,9},{5,8},{7,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,9},{3,8,12},{3,10,13},{4,5,12},{4,9,13},{4,10,11},{5,7,10},{5,8,13},
 {6,7,11},{6,10,12},{7,12,13},{8,9,11}}
 I={{0,13},{1,12},{2,10},{3,11},{4,7},{5,9},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 39 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,12},{2,10,0},{3,6,9},{3,8,13},{3,10,12},{3,11,0},
 {4,5,10},{4,7,11},{4,9,0},{4,12,13},{5,7,0},{5,8,12},{5,9,13},{6,7,12},
 {6,8,0},{6,10,11},{7,10,13},{8,9,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,12},{2,10,1},{3,6,9},{3,8,13},{3,10,12},{3,11,1},
 {4,5,10},{4,7,11},{4,9,1},{4,12,13},{5,7,1},{5,8,12},{5,9,13},{6,7,12},
 {6,8,1},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 9 5 12)(1 10 13 3)(2 7 8 11)(4)(6)
      B_1={{0,9,10},{2,3,7},{2,9,12},{3,6,9},{3,10,12},{3,11,1},
      {4,7,11},{4,9,1},{4,12,13},{5,8,12},{6,7,12},{6,10,11},
      {7,10,13},{8,9,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,13},{3,10,12},{3,11,2},
 {4,5,10},{4,7,11},{4,9,2},{4,12,13},{5,7,2},{5,8,12},{5,9,13},{6,7,12},
 {6,8,2},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,1},{3,7},{4,8},{5,11},{6,13},{9,12},{10,2}}
 Examples of antimorphisms:
   A: \alpha=(0 4 11 10)(1 8 6 9)(2 13 12 5)(3 7)
      B_1={{0,3,4},{0,11,12},{0,13,2},{1,3,5},{1,4,6},{1,8,10},
      {3,6,9},{3,8,13},{3,10,12},{3,11,2},{4,9,2},{5,8,12},
      {5,9,13},{6,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,13},{2,9,12},{2,10,3},
 {4,5,10},{4,7,11},{4,9,3},{4,12,13},{5,7,3},{5,8,12},{5,9,13},{6,7,12},
 {6,8,3},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,4},{1,5},{2,7},{6,9},{8,13},{10,12},{11,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{2,10,4},
 {3,6,9},{3,8,13},{3,10,12},{3,11,4},{5,7,4},{5,8,12},{5,9,13},{6,7,12},
 {6,8,4},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,3},{1,6},{2,8},{5,10},{7,11},{9,4},{12,13}}
 Examples of antimorphisms:
   B: \alpha=(0 1 8 5)(2 10 3 6)(4 12 9 13)(7 11)
      B_1={{0,1,2},{0,11,12},{0,13,4},{1,3,5},{1,11,13},{2,3,7},
      {2,5,11},{2,6,13},{2,9,12},{3,8,13},{3,10,12},{3,11,4},
      {5,8,12},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,10,5},
 {3,6,9},{3,8,13},{3,10,12},{3,11,5},{4,7,11},{4,9,5},{4,12,13},{6,7,12},
 {6,8,5},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,5},{8,12},{9,13}}
 Examples of antimorphisms:
   A: \alpha=(0 3 12 6 1 8)(2 9 11 13)(4 10 7)(5)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{0,13,5},{1,7,9},
      {1,8,10},{1,11,13},{1,12,5},{2,9,12},{4,9,5},{4,12,13},
      {6,7,12},{7,10,13}}
   B: \alpha=(0 6)(1 3)(2 9 11 13)(4 10)(5)(7)(8 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},
      {1,7,9},{1,11,13},{1,12,5},{2,9,12},{3,10,12},{4,9,5},
      {4,12,13},{7,10,13}}
   C: \alpha=(0 3 12 6 1 8)(2 13 11 9)(4 10 7)(5)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{0,13,5},{1,7,9},
      {1,8,10},{1,11,13},{1,12,5},{2,9,12},{4,9,5},{4,12,13},
      {6,7,12},{7,10,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,6},
 {3,8,13},{3,10,12},{3,11,6},{4,5,10},{4,7,11},{4,9,6},{4,12,13},{5,7,6},
 {5,8,12},{5,9,13},{7,10,13},{8,9,11}}
 I={{0,5},{1,4},{2,13},{3,9},{7,12},{8,6},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},{2,10,7},
 {3,6,9},{3,8,13},{3,10,12},{3,11,7},{4,5,10},{4,9,7},{4,12,13},{5,8,12},
 {5,9,13},{6,8,7},{6,10,11},{8,9,11}}
 I={{0,8},{1,9},{2,3},{4,11},{5,7},{6,12},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{2,10,8},
 {3,6,9},{3,10,12},{3,11,8},{4,5,10},{4,7,11},{4,9,8},{4,12,13},{5,7,8},
 {5,9,13},{6,7,12},{6,10,11},{7,10,13}}
 I={{0,7},{1,10},{2,4},{3,13},{5,12},{6,8},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,9},
 {3,8,13},{3,10,12},{3,11,9},{4,5,10},{4,7,11},{4,12,13},{5,7,9},{5,8,12},
 {6,7,12},{6,8,9},{6,10,11},{7,10,13}}
 I={{0,10},{1,7},{2,12},{3,6},{4,9},{5,13},{8,11}}
 Examples of antimorphisms:
   B: \alpha=(0 7 3 12)(1 6 2 10)(4 13 9 5)(8 11)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,9},{1,3,5},{1,8,10},
      {1,12,9},{2,3,7},{2,4,8},{2,6,13},{3,11,9},{4,5,10},
      {4,7,11},{6,8,9}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,9},{3,8,13},{3,11,10},{4,7,11},{4,9,10},{4,12,13},{5,7,10},{5,8,12},
 {5,9,13},{6,7,12},{6,8,10},{8,9,11}}
 I={{0,9},{1,8},{2,10},{3,12},{4,5},{6,11},{7,13}}
 Examples of antimorphisms:
   A: \alpha=(0 8 5 10 2 13 1 3 6 11)(4 9 12 7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,12,10},{2,4,8},{2,5,11},{2,6,13},{4,9,10},{4,12,13},
      {5,8,12},{6,7,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,10,11},
 {3,6,9},{3,8,13},{3,10,12},{4,5,10},{4,9,11},{4,12,13},{5,7,11},{5,8,12},
 {5,9,13},{6,7,12},{6,8,11},{7,10,13}}
 I={{0,12},{1,13},{2,5},{3,11},{4,7},{6,10},{8,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,12},
 {3,6,9},{3,8,13},{3,11,12},{4,5,10},{4,7,11},{4,9,12},{5,7,12},{5,9,13},
 {6,8,12},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,11},{1,12},{2,9},{3,10},{4,13},{5,8},{6,7}}
 Examples of antimorphisms:
   B: \alpha=(0 11)(1 4 12 13)(2 9)(3)(5 8)(6 7)(10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,13,12},{1,4,6},{1,8,10},
      {2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,12},{3,8,13},
      {6,8,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,13},
 {3,6,9},{3,10,12},{3,11,13},{4,5,10},{4,7,11},{4,9,13},{5,7,13},{5,8,12},
 {6,7,12},{6,8,13},{6,10,11},{8,9,11}}
 I={{0,13},{1,11},{2,6},{3,8},{4,12},{5,9},{7,10}}
 Examples of antimorphisms:
   A: \alpha=(0 9 7 13 4 11)(1 5 12 10)(2 6)(3 8)
      B_1={{0,5,6},{0,11,12},{1,4,6},{1,7,9},{1,8,10},{1,12,13},
      {3,6,9},{3,11,13},{4,9,13},{5,8,12},{6,7,12},{6,8,13},
      {6,10,11},{8,9,11}}
   B: \alpha=(0 1 12 6)(2 13 11 4)(3 7 8 10)(5 9)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,7,9},{1,8,10},{2,3,7},
      {2,4,8},{2,5,11},{2,9,12},{3,6,9},{3,11,13},{6,7,12},
      {6,10,11},{8,9,11}}
   C: \alpha=(0 4 2 6 7 13 1 3 8 9)(5 11 10 12)
      B_1={{0,3,4},{0,11,12},{1,4,6},{1,12,13},{2,5,11},{2,9,12},
      {3,6,9},{3,10,12},{3,11,13},{4,7,11},{4,9,13},{6,7,12},
      {6,8,13},{8,9,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,9},{3,8,13},{3,10,12},{4,5,10},{4,7,11},{4,12,13},{5,8,12},{5,9,13},
 {6,7,12},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,13},{1,12},{2,10},{3,11},{4,9},{5,7},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 40 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,12},{2,10,0},{3,6,12},{3,8,11},{3,9,0},{3,10,13},
 {4,5,0},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{6,7,10},
 {6,8,0},{6,9,11},{7,11,0},{8,12,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 9 13 10)(1 2)(3 4)(5 7 6 8)(11)(12)
      B_1={{1,3,5},{1,4,6},{2,5,11},{2,6,13},{2,9,12},{2,10,0},
      {3,6,12},{4,5,0},{4,9,13},{4,10,11},{5,7,13},{5,10,12},
      {6,8,0},{6,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,12},{2,10,1},{3,6,12},{3,8,11},{3,9,1},{3,10,13},
 {4,5,1},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{6,7,10},
 {6,8,1},{6,9,11},{7,11,1},{8,12,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,12},{3,8,11},{3,9,2},{3,10,13},
 {4,5,2},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{6,7,10},
 {6,8,2},{6,9,11},{7,11,2},{8,12,13}}
 I={{0,1},{3,7},{4,8},{5,11},{6,13},{9,12},{10,2}}
 Examples of antimorphisms:
   A: \alpha=(0 4 10 6)(1 11 7 13 2 5 3 8)(9)(12)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},
      {1,7,9},{1,8,10},{3,9,2},{3,10,13},{4,10,11},{5,10,12},
      {7,11,2},{8,12,13}}
   B: \alpha=(0 4 10 6)(1 8 2 13)(3 11 7 5)(9)(12)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},
      {1,7,9},{1,8,10},{1,12,2},{3,9,2},{3,10,13},{5,10,12},
      {6,7,10},{7,11,2}}
   C: \alpha=(0 6 11 12 8 10 5 9)(1 2 4 13)(3)(7)
      B_1={{0,7,8},{0,9,10},{0,13,2},{1,11,13},{3,6,12},{3,9,2},
      {3,10,13},{4,5,2},{5,7,13},{5,10,12},{6,8,2},{6,9,11},
      {7,11,2},{8,12,13}}
   D: \alpha=(0 10 8 6)(1 2 4 13)(3)(5 9 11 12)(7)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,11,12},{1,3,5},{1,4,6},
      {1,7,9},{1,8,10},{1,11,13},{3,8,11},{4,5,2},{4,7,12},
      {4,10,11},{5,8,9}}
 # of antimorphisms of SASC-graph: 16 (fair: 4) 
 # of halving permutations: 5 (fair: 1; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,13},{2,9,12},{2,10,3},
 {4,5,3},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{6,7,10},
 {6,8,3},{6,9,11},{7,11,3},{8,12,13}}
 I={{0,4},{1,5},{2,7},{6,12},{8,11},{9,3},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 6 8 10)(1 9 4 12)(2 7)(3 11 13 5)
      B_1={{0,5,6},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{2,5,11},
      {2,6,13},{2,10,3},{4,5,3},{4,7,12},{4,10,11},{5,10,12},
      {6,7,10},{6,9,11}}
   C: \alpha=(0 6 8 10)(1 13 4 3)(2)(5 12 11 9)(7)
      B_1={{0,9,10},{0,13,3},{1,12,3},{2,6,13},{2,9,12},{2,10,3},
      {4,9,13},{5,7,13},{5,10,12},{6,7,10},{6,8,3},{6,9,11},
      {7,11,3},{8,12,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{2,10,4},
 {3,6,12},{3,8,11},{3,9,4},{3,10,13},{5,7,13},{5,8,9},{5,10,12},{6,7,10},
 {6,8,4},{6,9,11},{7,11,4},{8,12,13}}
 I={{0,3},{1,6},{2,8},{5,4},{7,12},{9,13},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 3)(1 6)(2 10 7 8 11 12)(4 13 9)(5)
      B_1={{1,3,5},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{3,6,12},
      {3,8,11},{3,9,4},{3,10,13},{5,7,13},{6,7,10},{6,8,4},
      {6,9,11},{7,11,4}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,10,5},
 {3,6,12},{3,8,11},{3,9,5},{3,10,13},{4,7,12},{4,9,13},{4,10,11},{6,7,10},
 {6,8,5},{6,9,11},{7,11,5},{8,12,13}}
 I={{0,6},{1,3},{2,11},{4,5},{7,13},{8,9},{10,12}}
 Examples of antimorphisms:
   B: \alpha=(0 7 6 13)(1 3)(2 4 9 10)(5 8 12 11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{1,4,6},{1,7,9},
      {1,8,10},{1,11,13},{1,12,5},{2,4,8},{2,6,13},{4,10,11},
      {6,8,5},{6,9,11}}
   D: \alpha=(0 13 6 7)(1 3)(2 10 9 4)(5 11 12 8)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{1,4,6},{1,7,9},
      {1,8,10},{1,11,13},{1,12,5},{2,4,8},{2,6,13},{4,10,11},
      {6,8,5},{6,9,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,6},
 {3,8,11},{3,9,6},{3,10,13},{4,5,6},{4,7,12},{4,9,13},{4,10,11},{5,7,13},
 {5,8,9},{5,10,12},{7,11,6},{8,12,13}}
 I={{0,5},{1,4},{2,13},{3,12},{7,10},{8,6},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},{2,10,7},
 {3,6,12},{3,8,11},{3,9,7},{3,10,13},{4,5,7},{4,9,13},{4,10,11},{5,8,9},
 {5,10,12},{6,8,7},{6,9,11},{8,12,13}}
 I={{0,8},{1,9},{2,3},{4,12},{5,13},{6,10},{11,7}}
 Examples of antimorphisms:
   B: \alpha=(0 6 8 10)(1 13 4 7)(2)(3)(5 12 11 9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,8,10},{1,11,13},{2,4,8},{2,5,11},{3,8,11},{4,5,7},
      {4,10,11},{5,8,9}}
   D: \alpha=(0 10 8 6)(1 7 4 13)(2)(3)(5 9 11 12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,4,6},
      {1,8,10},{1,11,13},{2,4,8},{2,5,11},{3,8,11},{4,5,7},
      {4,10,11},{5,8,9}}
 # of antimorphisms of SASC-graph: 6 (fair: 6) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{2,10,8},
 {3,6,12},{3,9,8},{3,10,13},{4,5,8},{4,7,12},{4,9,13},{4,10,11},{5,7,13},
 {5,10,12},{6,7,10},{6,9,11},{7,11,8}}
 I={{0,7},{1,10},{2,4},{3,11},{5,9},{6,8},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 3 12 9 10 13)(1 8 4 11)(2 5 7 6)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,12,8},
      {2,5,11},{2,10,8},{3,6,12},{4,7,12},{4,10,11},{5,10,12},
      {6,7,10},{7,11,8}}
   C: \alpha=(0 7)(1 2 13 9)(3 8 5 10)(4 12 11 6)
      B_1={{1,3,5},{1,7,9},{1,12,8},{2,3,7},{2,6,13},{2,9,12},
      {3,10,13},{4,5,8},{4,7,12},{4,10,11},{5,7,13},{6,7,10},
      {6,9,11},{7,11,8}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,9},
 {3,6,12},{3,8,11},{3,10,13},{4,5,9},{4,7,12},{4,10,11},{5,7,13},{5,10,12},
 {6,7,10},{6,8,9},{7,11,9},{8,12,13}}
 I={{0,10},{1,7},{2,12},{3,9},{4,13},{5,8},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 8 11 13)(1 4 10 3)(2 12)(5 6 9 7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,9},{1,3,5},
      {1,12,9},{2,5,11},{2,10,9},{3,8,11},{4,5,9},{4,10,11},
      {5,10,12},{7,11,9}}
   C: \alpha=(0 8 11 13)(1 4 10 3)(2)(5 6 9 7)(12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,9},{1,3,5},
      {1,12,9},{2,5,11},{2,10,9},{3,8,11},{4,5,9},{4,10,11},
      {5,10,12},{7,11,9}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,12},{3,8,11},{3,9,10},{4,5,10},{4,7,12},{4,9,13},{5,7,13},{5,8,9},
 {6,8,10},{6,9,11},{7,11,10},{8,12,13}}
 I={{0,9},{1,8},{2,10},{3,13},{4,11},{5,12},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 9)(1 8)(2 5 3 10 12 13)(4 6 11)(7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},
      {1,3,5},{1,4,6},{1,11,13},{1,12,10},{2,6,13},{4,5,10},
      {5,7,13},{7,11,10}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,10,11},
 {3,6,12},{3,9,11},{3,10,13},{4,5,11},{4,7,12},{4,9,13},{5,7,13},{5,8,9},
 {5,10,12},{6,7,10},{6,8,11},{8,12,13}}
 I={{0,12},{1,13},{2,5},{3,8},{4,10},{6,9},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,12},
 {3,8,11},{3,9,12},{3,10,13},{4,5,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},
 {6,7,10},{6,8,12},{6,9,11},{7,11,12}}
 I={{0,11},{1,12},{2,9},{3,6},{4,7},{5,10},{8,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 6 8 11 10 12 3 4 13 5)(2 9)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,13,12},{1,8,10},{2,3,7},
      {2,4,8},{2,5,11},{2,6,13},{2,10,12},{3,8,11},{3,10,13},
      {5,7,13},{6,7,10}}
   B: \alpha=(0 4 10 6)(1 8 12 13)(2)(3 11 7 5)(9)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,13,12},{1,3,5},
      {1,7,9},{1,8,10},{2,3,7},{2,10,12},{3,9,12},{3,10,13},
      {6,7,10},{7,11,12}}
   D: \alpha=(0 8 11 13)(1 4 10 3)(2)(5 6 12 7)(9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,13,12},{1,3,5},{2,5,11},
      {2,10,12},{3,8,11},{3,9,12},{4,5,12},{4,9,13},{4,10,11},
      {5,8,9},{7,11,12}}
 # of antimorphisms of SASC-graph: 12 (fair: 8) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,13},
 {3,6,12},{3,8,11},{3,9,13},{4,5,13},{4,7,12},{4,10,11},{5,8,9},{5,10,12},
 {6,7,10},{6,8,13},{6,9,11},{7,11,13}}
 I={{0,13},{1,11},{2,6},{3,10},{4,9},{5,7},{8,12}}
 Examples of antimorphisms:
   C: \alpha=(0 13)(1 11)(2 4 5 6 9 7)(3 8 10)(12)
      B_1={{1,12,13},{2,3,7},{2,5,11},{2,9,12},{2,10,13},{3,8,11},
      {3,9,13},{4,5,13},{4,10,11},{5,8,9},{5,10,12},{6,8,13},
      {6,9,11},{7,11,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,12},{3,8,11},{3,10,13},{4,7,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},
 {5,10,12},{6,7,10},{6,9,11},{8,12,13}}
 I={{0,13},{1,12},{2,10},{3,9},{4,5},{6,8},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 41 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,12},{2,10,0},{3,6,10},{3,8,11},{3,9,0},{3,12,13},
 {4,5,9},{4,7,13},{4,10,12},{4,11,0},{5,7,0},{5,8,12},{5,10,13},{6,7,12},
 {6,8,0},{6,9,11},{7,10,11},{8,9,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,12},{2,10,1},{3,6,10},{3,8,11},{3,9,1},{3,12,13},
 {4,5,9},{4,7,13},{4,10,12},{4,11,1},{5,7,1},{5,8,12},{5,10,13},{6,7,12},
 {6,8,1},{6,9,11},{7,10,11},{8,9,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 7 9 10 11 12 6 4 5 13)(1 8 2 3)
      B_1={{0,5,6},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,5,11},
      {2,6,13},{2,9,12},{2,10,1},{4,5,9},{4,11,1},{5,7,1},
      {6,8,1},{6,9,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,10},{3,8,11},{3,9,2},{3,12,13},
 {4,5,9},{4,7,13},{4,10,12},{4,11,2},{5,7,2},{5,8,12},{5,10,13},{6,7,12},
 {6,8,2},{6,9,11},{7,10,11},{8,9,13}}
 I={{0,1},{3,7},{4,8},{5,11},{6,13},{9,12},{10,2}}
 Examples of antimorphisms:
   C: \alpha=(0 4 11 7 9 6 12 13)(1 3 2 8 5 10)
      B_1={{0,3,4},{0,7,8},{0,9,10},{0,11,12},{1,8,10},{3,6,10},
      {3,8,11},{3,9,2},{3,12,13},{4,10,12},{5,8,12},{6,9,11},
      {7,10,11},{8,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,13},{2,9,12},{2,10,3},
 {4,5,9},{4,7,13},{4,10,12},{4,11,3},{5,7,3},{5,8,12},{5,10,13},{6,7,12},
 {6,8,3},{6,9,11},{7,10,11},{8,9,13}}
 I={{0,4},{1,5},{2,7},{6,10},{8,11},{9,3},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{2,10,4},
 {3,6,10},{3,8,11},{3,9,4},{3,12,13},{5,7,4},{5,8,12},{5,10,13},{6,7,12},
 {6,8,4},{6,9,11},{7,10,11},{8,9,13}}
 I={{0,3},{1,6},{2,8},{5,9},{7,13},{10,12},{11,4}}
 Examples of antimorphisms:
   C: \alpha=(0 1 13 10)(2 11 6 7)(3 8 4 12)(5 9)
      B_1={{0,1,2},{0,5,6},{1,3,5},{1,8,10},{1,12,4},{2,5,11},
      {2,6,13},{2,10,4},{3,6,10},{3,8,11},{3,9,4},{5,7,4},
      {5,10,13},{6,7,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,10,5},
 {3,6,10},{3,8,11},{3,9,5},{3,12,13},{4,7,13},{4,10,12},{4,11,5},{6,7,12},
 {6,8,5},{6,9,11},{7,10,11},{8,9,13}}
 I={{0,6},{1,3},{2,11},{4,9},{7,5},{8,12},{10,13}}
 Examples of antimorphisms:
   C: \alpha=(0 6)(1 3)(2 10 8 11 13 12)(4)(5 7 9)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},
      {1,7,9},{1,8,10},{1,11,13},{1,12,5},{2,9,12},{4,10,12},
      {4,11,5},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,6},
 {3,8,11},{3,9,6},{3,12,13},{4,5,9},{4,7,13},{4,10,12},{4,11,6},{5,7,6},
 {5,8,12},{5,10,13},{7,10,11},{8,9,13}}
 I={{0,5},{1,4},{2,13},{3,10},{7,12},{8,6},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},{2,10,7},
 {3,6,10},{3,8,11},{3,9,7},{3,12,13},{4,5,9},{4,10,12},{4,11,7},{5,8,12},
 {5,10,13},{6,8,7},{6,9,11},{8,9,13}}
 I={{0,8},{1,9},{2,3},{4,13},{5,7},{6,12},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 8)(1 9)(2 5 4 3 7 13)(6 11 12)(10)
      B_1={{1,8,10},{2,4,8},{2,6,13},{2,9,12},{2,10,7},{3,8,11},
      {3,9,7},{4,5,9},{4,10,12},{4,11,7},{5,8,12},{6,8,7},
      {6,9,11},{8,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,5,11},{2,6,13},{2,9,12},{2,10,8},
 {3,6,10},{3,9,8},{3,12,13},{4,5,9},{4,7,13},{4,10,12},{4,11,8},{5,7,8},
 {5,10,13},{6,7,12},{6,9,11},{7,10,11}}
 I={{0,7},{1,10},{2,4},{3,11},{5,12},{6,8},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,9},
 {3,6,10},{3,8,11},{3,12,13},{4,7,13},{4,10,12},{4,11,9},{5,7,9},{5,8,12},
 {5,10,13},{6,7,12},{6,8,9},{7,10,11}}
 I={{0,10},{1,7},{2,12},{3,9},{4,5},{6,11},{8,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,8,11},{3,9,10},{3,12,13},{4,5,9},{4,7,13},{4,11,10},{5,7,10},{5,8,12},
 {6,7,12},{6,8,10},{6,9,11},{8,9,13}}
 I={{0,9},{1,8},{2,10},{3,6},{4,12},{5,13},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 4 7 5 3 9 12 8 11 6 13)(2 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,13,10},{1,4,6},{1,12,10},
      {3,9,10},{4,5,9},{4,11,10},{5,7,10},{5,8,12},{6,8,10},
      {6,9,11},{8,9,13}}
   B: \alpha=(0 3 12 5)(1 7 8 11)(2)(4 13 9 6)(10)
      B_1={{0,1,2},{0,3,4},{1,3,5},{1,4,6},{1,7,9},{2,4,8},
      {2,9,12},{3,8,11},{3,9,10},{4,5,9},{4,11,10},{5,7,10},
      {5,8,12},{8,9,13}}
   C: \alpha=(0 3 6 7 8 1 9 13 5 11 4 12)(2 10)
      B_1={{0,1,2},{0,11,12},{1,3,5},{1,7,9},{1,11,13},{2,3,7},
      {2,4,8},{2,5,11},{2,6,13},{2,9,12},{3,8,11},{3,12,13},
      {4,7,13},{6,7,12}}
 # of antimorphisms of SASC-graph: 8 (fair: 4) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,10,11},
 {3,6,10},{3,9,11},{3,12,13},{4,5,9},{4,7,13},{4,10,12},{5,7,11},{5,8,12},
 {5,10,13},{6,7,12},{6,8,11},{8,9,13}}
 I={{0,12},{1,13},{2,5},{3,8},{4,11},{6,9},{7,10}}
 Examples of antimorphisms:
   A: \alpha=(0 2 7 11)(1 13)(3 9 4 12)(5 10 8 6)
      B_1={{0,3,4},{0,9,10},{0,13,11},{2,3,7},{2,6,13},{2,10,11},
      {3,12,13},{4,5,9},{4,7,13},{5,8,12},{5,10,13},{6,7,12},
      {6,8,11},{8,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,12},
 {3,6,10},{3,8,11},{3,9,12},{4,5,9},{4,7,13},{4,11,12},{5,7,12},{5,10,13},
 {6,8,12},{6,9,11},{7,10,11},{8,9,13}}
 I={{0,11},{1,12},{2,9},{3,13},{4,10},{5,8},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 11)(1 12)(2 4 6 9 10 7)(3 8 5)(13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},
      {1,3,5},{1,4,6},{1,7,9},{1,8,10},{2,3,7},{4,5,9},
      {4,7,13},{8,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,13},
 {3,6,10},{3,8,11},{3,9,13},{4,5,9},{4,10,12},{4,11,13},{5,7,13},{5,8,12},
 {6,7,12},{6,8,13},{6,9,11},{7,10,11}}
 I={{0,13},{1,11},{2,6},{3,12},{4,7},{5,10},{8,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,10},{3,8,11},{3,12,13},{4,5,9},{4,7,13},{4,10,12},{5,8,12},{5,10,13},
 {6,7,12},{6,9,11},{7,10,11},{8,9,13}}
 I={{0,13},{1,12},{2,10},{3,9},{4,11},{5,7},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 3 12 5)(1 7 8 11)(2)(4 13 9 6)(10)
      B_1={{0,5,6},{0,7,8},{0,11,12},{1,11,13},{2,3,7},{2,5,11},
      {2,6,13},{3,6,10},{3,12,13},{4,7,13},{5,10,13},{6,7,12},
      {6,9,11},{7,10,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 42 
 |Aut(S)|=2 


 Subsystem No. 0 
 |Aut(T)|=2 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,0},{2,10,12},{3,6,9},{3,8,12},{3,10,13},{3,11,0},
 {4,5,10},{4,7,0},{4,9,11},{4,12,13},{5,7,13},{5,8,0},{5,9,12},{6,7,12},
 {6,8,11},{6,10,0},{7,10,11},{8,9,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 6 1 7)(2 9 3 5)(4 8 13 10)(11 12)
      B_1={{1,3,5},{1,7,9},{1,8,10},{2,4,8},{2,9,0},{2,10,12},
      {3,8,12},{3,10,13},{5,8,0},{5,9,12},{6,7,12},{6,8,11},
      {6,10,0},{7,10,11}}
   B: \alpha=(0 13)(1)(2)(3 4)(5 6)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,7},{2,5,11},{2,9,0},
      {3,6,9},{3,11,0},{4,7,0},{4,9,11},{5,8,0},{6,8,11},
      {6,10,0},{7,10,11}}
 # of antimorphisms of SASC-graph: 7 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,1},{2,10,12},{3,6,9},{3,8,12},{3,10,13},{3,11,1},
 {4,5,10},{4,7,1},{4,9,11},{4,12,13},{5,7,13},{5,8,1},{5,9,12},{6,7,12},
 {6,8,11},{6,10,1},{7,10,11},{8,9,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,12},{3,10,13},{3,11,2},
 {4,5,10},{4,7,2},{4,9,11},{4,12,13},{5,7,13},{5,8,2},{5,9,12},{6,7,12},
 {6,8,11},{6,10,2},{7,10,11},{8,9,13}}
 I={{0,1},{3,7},{4,8},{5,11},{6,13},{9,2},{10,12}}
 Examples of antimorphisms:
   B: \alpha=(0 7 4 9)(1 3 8 2)(5 12 11 10)(6)(13)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,2},{1,8,10},{1,12,2},
      {3,6,9},{3,8,12},{3,10,13},{4,5,10},{4,7,2},{4,12,13},
      {6,7,12},{6,10,2}}
   D: \alpha=(0 9 4 7)(1 2 8 3)(5 10 11 12)(6)(13)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,2},{1,8,10},{1,12,2},
      {3,6,9},{3,8,12},{3,10,13},{4,5,10},{4,7,2},{4,12,13},
      {6,7,12},{6,10,2}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 2 (fair: 2; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,13},{2,9,3},{2,10,12},
 {4,5,10},{4,7,3},{4,9,11},{4,12,13},{5,7,13},{5,8,3},{5,9,12},{6,7,12},
 {6,8,11},{6,10,3},{7,10,11},{8,9,13}}
 I={{0,4},{1,5},{2,7},{6,9},{8,12},{10,13},{11,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,13},{2,9,5},{2,10,12},
 {3,6,9},{3,8,12},{3,10,13},{3,11,5},{4,7,5},{4,9,11},{4,12,13},{6,7,12},
 {6,8,11},{6,10,5},{7,10,11},{8,9,13}}
 I={{0,6},{1,3},{2,11},{4,10},{7,13},{8,5},{9,12}}
 Examples of antimorphisms:
   C: \alpha=(0 8 3 10)(1 4 7 12)(2)(5 13 9 6)(11)
      B_1={{0,7,8},{1,4,6},{1,8,10},{1,11,13},{2,4,8},{2,9,5},
      {2,10,12},{3,10,13},{4,12,13},{6,7,12},{6,8,11},{6,10,5},
      {7,10,11},{8,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,13},{2,9,7},{2,10,12},
 {3,6,9},{3,8,12},{3,10,13},{3,11,7},{4,5,10},{4,9,11},{4,12,13},{5,8,7},
 {5,9,12},{6,8,11},{6,10,7},{8,9,13}}
 I={{0,8},{1,9},{2,3},{4,7},{5,13},{6,12},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,12},
 {3,8,12},{3,10,13},{3,11,9},{4,5,10},{4,7,9},{4,12,13},{5,7,13},{5,8,9},
 {6,7,12},{6,8,11},{6,10,9},{7,10,11}}
 I={{0,10},{1,7},{2,9},{3,6},{4,11},{5,12},{8,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,13},{2,9,11},{2,10,12},
 {3,6,9},{3,8,12},{3,10,13},{4,5,10},{4,7,11},{4,12,13},{5,7,13},{5,8,11},
 {5,9,12},{6,7,12},{6,10,11},{8,9,13}}
 I={{0,12},{1,13},{2,5},{3,11},{4,9},{6,8},{7,10}}
 Examples of antimorphisms:
   A: \alpha=(0 8 3 10)(1 4 7 12)(2 5)(6 11 13 9)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,13,11},{1,3,5},{1,4,6},
      {1,8,10},{2,3,7},{2,6,13},{3,6,9},{3,10,13},{4,12,13},
      {5,7,13},{6,7,12}}
   C: \alpha=(0 8 3 10)(1 4 7 12)(2)(5)(6 11 13 9)
      B_1={{0,5,6},{0,7,8},{1,3,5},{1,4,6},{1,8,10},{2,4,8},
      {2,9,11},{2,10,12},{3,10,13},{4,12,13},{5,7,13},{6,7,12},
      {6,10,11},{8,9,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,9},{3,10,13},{3,11,12},{4,5,10},{4,7,12},{4,9,11},{5,7,13},{5,8,12},
 {6,8,11},{6,10,12},{7,10,11},{8,9,13}}
 I={{0,11},{1,12},{2,10},{3,8},{4,13},{5,9},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 11)(1 6 3 7 12 8)(2 4 9 10 13 5)
      B_1={{1,4,6},{1,7,9},{1,11,13},{2,3,7},{2,5,11},{2,6,13},
      {2,9,12},{3,10,13},{3,11,12},{4,9,11},{5,8,12},{6,8,11},
      {7,10,11},{8,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 43 
 |Aut(S)|=6 


 Subsystem No. 0 
 |Aut(T)|=2 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,0},{2,10,12},{3,6,9},{3,8,0},{3,10,11},{3,12,13},
 {4,5,10},{4,7,12},{4,9,13},{4,11,0},{5,7,0},{5,8,13},{5,9,12},{6,7,11},
 {6,8,12},{6,10,0},{7,10,13},{8,9,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 7 11 13 8 12)(1 5 6)(2)(3 4)(9 10)
      B_1={{1,4,6},{1,8,10},{1,12,0},{2,4,8},{2,5,11},{2,9,0},
      {3,8,0},{3,10,11},{4,5,10},{4,11,0},{5,8,13},{6,7,11},
      {6,10,0},{8,9,11}}
   B: \alpha=(0 13)(1)(2)(3 4)(5 6)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,7},{2,5,11},{2,9,0},
      {3,6,9},{3,8,0},{3,10,11},{3,12,13},{5,7,0},{6,7,11},
      {6,10,0},{8,9,11}}
   C: \alpha=(0 13)(1)(2 7 10 6 5 9 8)(3 4)(11 12)
      B_1={{1,4,6},{1,7,9},{1,12,0},{2,4,8},{2,6,13},{2,10,12},
      {4,5,10},{4,7,12},{4,9,13},{4,11,0},{5,8,13},{5,9,12},
      {6,8,12},{7,10,13}}
 # of antimorphisms of SASC-graph: 5 (fair: 1) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,1},{2,10,12},{3,6,9},{3,8,1},{3,10,11},{3,12,13},
 {4,5,10},{4,7,12},{4,9,13},{4,11,1},{5,7,1},{5,8,13},{5,9,12},{6,7,11},
 {6,8,12},{6,10,1},{7,10,13},{8,9,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,2},{3,10,11},{3,12,13},
 {4,5,10},{4,7,12},{4,9,13},{4,11,2},{5,7,2},{5,8,13},{5,9,12},{6,7,11},
 {6,8,12},{6,10,2},{7,10,13},{8,9,11}}
 I={{0,1},{3,7},{4,8},{5,11},{6,13},{9,2},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,13},{2,9,5},{2,10,12},
 {3,6,9},{3,8,5},{3,10,11},{3,12,13},{4,7,12},{4,9,13},{4,11,5},{6,7,11},
 {6,8,12},{6,10,5},{7,10,13},{8,9,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,5},{8,13},{9,12}}
 Examples of antimorphisms:
   B: \alpha=(0 8 6 13)(1)(2 5 4 12)(3)(7 10 9 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{1,4,6},{1,7,9},
      {2,3,7},{2,4,8},{2,6,13},{2,9,5},{3,6,9},{4,7,12},
      {4,9,13},{6,7,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 44 
 |Aut(S)|=2 


 Subsystem No. 0 
 |Aut(T)|=2 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,0},{2,10,12},{3,6,12},{3,8,11},{3,9,13},{3,10,0},
 {4,5,0},{4,7,13},{4,9,12},{4,10,11},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,0},{6,9,11},{7,11,0},{8,12,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 13)(1)(2 5 6)(3 4)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,7},{2,6,13},{2,10,12},
      {3,6,12},{3,9,13},{4,7,13},{4,9,12},{5,7,12},{5,10,13},
      {6,7,10},{7,11,0}}
   B: \alpha=(0 13)(1)(2)(3 4)(5 6)(7 8)(9 10)(11 12)
      B_1={{1,3,5},{1,7,9},{1,11,13},{2,3,7},{2,5,11},{2,9,0},
      {3,8,11},{3,10,0},{4,5,0},{4,10,11},{5,8,9},{6,8,0},
      {6,9,11},{7,11,0}}
 # of antimorphisms of SASC-graph: 5 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,13},{2,9,1},{2,10,12},{3,6,12},{3,8,11},{3,9,13},{3,10,1},
 {4,5,1},{4,7,13},{4,9,12},{4,10,11},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,1},{6,9,11},{7,11,1},{8,12,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=2 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,12},{3,8,11},{3,9,13},{3,10,2},
 {4,5,2},{4,7,13},{4,9,12},{4,10,11},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,2},{6,9,11},{7,11,2},{8,12,13}}
 I={{0,1},{3,7},{4,8},{5,11},{6,13},{9,2},{10,12}}
 Examples of antimorphisms:
   C: \alpha=(0 7 13 9)(1 6 12 4 3 10 8 2)(5)(11)
      B_1={{0,5,6},{0,9,10},{0,13,2},{1,4,6},{3,10,2},{4,5,2},
      {4,7,13},{4,9,12},{4,10,11},{5,10,13},{6,7,10},{6,8,2},
      {6,9,11},{7,11,2}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,13},{2,9,3},{2,10,12},
 {4,5,3},{4,7,13},{4,9,12},{4,10,11},{5,7,12},{5,8,9},{5,10,13},{6,7,10},
 {6,8,3},{6,9,11},{7,11,3},{8,12,13}}
 I={{0,4},{1,5},{2,7},{6,12},{8,11},{9,13},{10,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,13},{2,9,5},{2,10,12},
 {3,6,12},{3,8,11},{3,9,13},{3,10,5},{4,7,13},{4,9,12},{4,10,11},{6,7,10},
 {6,8,5},{6,9,11},{7,11,5},{8,12,13}}
 I={{0,6},{1,3},{2,11},{4,5},{7,12},{8,9},{10,13}}
 Examples of antimorphisms:
   C: \alpha=(0 3 6 10 1 13)(2 9 12 7 8 11)(4 5)
      B_1={{0,1,2},{0,7,8},{0,11,12},{0,13,5},{1,7,9},{1,8,10},
      {1,12,5},{2,6,13},{2,9,5},{3,6,12},{3,10,5},{6,8,5},
      {6,9,11},{7,11,5}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,13},{2,9,7},{2,10,12},
 {3,6,12},{3,8,11},{3,9,13},{3,10,7},{4,5,7},{4,9,12},{4,10,11},{5,8,9},
 {5,10,13},{6,8,7},{6,9,11},{8,12,13}}
 I={{0,8},{1,9},{2,3},{4,13},{5,12},{6,10},{11,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,12},
 {3,6,12},{3,8,11},{3,10,9},{4,5,9},{4,7,13},{4,10,11},{5,7,12},{5,10,13},
 {6,7,10},{6,8,9},{7,11,9},{8,12,13}}
 I={{0,10},{1,7},{2,9},{3,13},{4,12},{5,8},{6,11}}
 Examples of antimorphisms:
   C: \alpha=(0 4 1 11)(2 3 6 10)(5 8)(7 9 13 12)
      B_1={{0,3,4},{0,7,8},{1,8,10},{1,11,13},{2,4,8},{2,10,12},
      {3,6,12},{3,8,11},{3,10,9},{4,7,13},{4,10,11},{6,8,9},
      {7,11,9},{8,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,13},{2,9,11},{2,10,12},
 {3,6,12},{3,9,13},{3,10,11},{4,5,11},{4,7,13},{4,9,12},{5,7,12},{5,8,9},
 {5,10,13},{6,7,10},{6,8,11},{8,12,13}}
 I={{0,12},{1,13},{2,5},{3,8},{4,10},{6,9},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,8,11},{3,9,13},{3,10,12},{4,5,12},{4,7,13},{4,10,11},{5,8,9},{5,10,13},
 {6,7,10},{6,8,12},{6,9,11},{7,11,12}}
 I={{0,11},{1,12},{2,10},{3,6},{4,9},{5,7},{8,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 45 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,0},{2,9,12},{2,10,13},{3,6,9},{3,8,11},{3,10,0},{3,12,13},
 {4,5,0},{4,7,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},{6,7,12},
 {6,8,13},{6,10,11},{7,11,0},{8,9,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,1},{2,9,12},{2,10,13},{3,6,9},{3,8,11},{3,10,1},{3,12,13},
 {4,5,1},{4,7,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},{6,7,12},
 {6,8,13},{6,10,11},{7,11,1},{8,9,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,11},{3,10,2},{3,12,13},
 {4,5,2},{4,7,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},{6,7,12},
 {6,8,13},{6,10,11},{7,11,2},{8,9,2}}
 I={{0,1},{3,7},{4,8},{5,11},{6,2},{9,12},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1)(2 7 12 8 11 9)(3 4 6 5)(10 13)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{1,7,9},{1,8,10},
      {3,6,9},{3,8,11},{3,10,2},{4,10,12},{5,7,10},{6,7,12},
      {6,10,11},{8,9,2}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,3},{2,9,12},{2,10,13},
 {4,5,3},{4,7,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},{5,9,13},{6,7,12},
 {6,8,13},{6,10,11},{7,11,3},{8,9,3}}
 I={{0,4},{1,5},{2,7},{6,9},{8,11},{10,3},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,9,12},{2,10,13},
 {3,6,9},{3,8,11},{3,10,4},{3,12,13},{5,7,10},{5,8,12},{5,9,13},{6,7,12},
 {6,8,13},{6,10,11},{7,11,4},{8,9,4}}
 I={{0,3},{1,6},{2,8},{5,4},{7,13},{9,11},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,5},{2,9,12},{2,10,13},
 {3,6,9},{3,8,11},{3,10,5},{3,12,13},{4,7,13},{4,9,11},{4,10,12},{6,7,12},
 {6,8,13},{6,10,11},{7,11,5},{8,9,5}}
 I={{0,6},{1,3},{2,11},{4,5},{7,10},{8,12},{9,13}}
 Examples of antimorphisms:
   C: \alpha=(0)(1 3)(2 4 9 7)(5 10 8 11 13 12)(6)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,4,6},{1,7,9},{1,8,10},
      {1,11,13},{1,12,5},{2,4,8},{4,7,13},{4,10,12},{6,7,12},
      {6,10,11},{7,11,5}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,13},
 {3,8,11},{3,10,6},{3,12,13},{4,5,6},{4,7,13},{4,9,11},{4,10,12},{5,7,10},
 {5,8,12},{5,9,13},{7,11,6},{8,9,6}}
 I={{0,5},{1,4},{2,6},{3,9},{7,12},{8,13},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,7},{2,9,12},{2,10,13},
 {3,6,9},{3,8,11},{3,10,7},{3,12,13},{4,5,7},{4,9,11},{4,10,12},{5,8,12},
 {5,9,13},{6,8,13},{6,10,11},{8,9,7}}
 I={{0,8},{1,9},{2,3},{4,13},{5,10},{6,12},{11,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,5,11},{2,6,8},{2,9,12},{2,10,13},
 {3,6,9},{3,10,8},{3,12,13},{4,5,8},{4,7,13},{4,9,11},{4,10,12},{5,7,10},
 {5,9,13},{6,7,12},{6,10,11},{7,11,8}}
 I={{0,7},{1,10},{2,4},{3,11},{5,12},{6,13},{9,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,9},{2,10,13},
 {3,8,11},{3,10,9},{3,12,13},{4,5,9},{4,7,13},{4,10,12},{5,7,10},{5,8,12},
 {6,7,12},{6,8,13},{6,10,11},{7,11,9}}
 I={{0,10},{1,7},{2,12},{3,6},{4,11},{5,13},{8,9}}
 Examples of antimorphisms:
   A: \alpha=(0 7 13 12)(1 5 11 6)(2 10 4 3)(8 9)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,9},{1,3,5},{1,8,10},
      {1,11,13},{1,12,9},{2,4,8},{2,10,13},{3,8,11},{4,7,13},
      {6,10,11},{7,11,9}}
   B: \alpha=(0 10)(1 7)(2 12)(3 6)(4 11)(5 13)(8)(9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},
      {1,3,5},{1,11,13},{2,3,7},{2,5,11},{2,6,9},{3,8,11},
      {5,8,12},{7,11,9}}
 # of antimorphisms of SASC-graph: 3 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,8},{2,5,11},{2,6,10},{2,9,12},
 {3,6,9},{3,8,11},{3,12,13},{4,5,10},{4,7,13},{4,9,11},{5,8,12},{5,9,13},
 {6,7,12},{6,8,13},{7,11,10},{8,9,10}}
 I={{0,9},{1,8},{2,13},{3,10},{4,12},{5,7},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 6 12 8)(1 9 13 11 4 2)(3 10)(5 7)
      B_1={{0,7,8},{1,4,6},{1,7,9},{1,11,13},{2,3,7},{2,4,8},
      {2,6,10},{3,6,9},{3,8,11},{4,7,13},{6,7,12},{6,8,13},
      {7,11,10},{8,9,10}}
   C: \alpha=(0 6 12 8)(1 9 13 11 4 2)(3)(5 7)(10)
      B_1={{0,7,8},{1,4,6},{1,7,9},{1,11,13},{2,3,7},{2,4,8},
      {2,6,10},{3,6,9},{3,8,11},{4,7,13},{6,7,12},{6,8,13},
      {7,11,10},{8,9,10}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,11},{2,9,12},{2,10,13},
 {3,6,9},{3,10,11},{3,12,13},{4,5,11},{4,7,13},{4,10,12},{5,7,10},{5,8,12},
 {5,9,13},{6,7,12},{6,8,13},{8,9,11}}
 I={{0,12},{1,13},{2,5},{3,8},{4,9},{6,10},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 8 13 9)(2 11 4 10)(3 6 5 12)
      B_1={{0,9,10},{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,12,11},
      {2,4,8},{2,6,11},{2,9,12},{3,6,9},{4,10,12},{5,8,12},
      {6,8,13},{8,9,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,12},{2,10,13},
 {3,6,9},{3,8,11},{3,10,12},{4,5,12},{4,7,13},{4,9,11},{5,7,10},{5,9,13},
 {6,8,13},{6,10,11},{7,11,12},{8,9,12}}
 I={{0,11},{1,12},{2,9},{3,13},{4,10},{5,8},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 1 4 11 12 5 2 6)(3)(7 8 10 9)(13)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,13,12},{2,3,7},
      {2,4,8},{2,6,12},{2,10,13},{3,10,12},{4,5,12},{4,7,13},
      {4,9,11},{8,9,12}}
   C: \alpha=(0 1 4 11 12 5 2 6)(3 13)(7 8 10 9)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,13,12},{2,3,7},
      {2,4,8},{2,6,12},{2,10,13},{3,10,12},{4,5,12},{4,7,13},
      {4,9,11},{8,9,12}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,9},{3,8,11},{3,10,13},{4,5,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},
 {6,7,12},{6,10,11},{7,11,13},{8,9,13}}
 I={{0,13},{1,11},{2,10},{3,12},{4,7},{5,9},{6,8}}
 Examples of antimorphisms:
   B: \alpha=(0 13)(1 11)(2 10)(3 12)(4)(5 9)(6 8)(7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},
      {1,7,9},{1,8,10},{2,3,7},{2,4,8},{2,9,12},{3,6,9},
      {3,8,11},{4,9,11}}
   C: \alpha=(0 2 5 3 6 7 8 4 13 10 9 12)(1 11)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,11,12},{2,5,11},{2,6,13},
      {3,6,9},{3,8,11},{4,5,13},{4,9,11},{5,8,12},{6,10,11},
      {7,11,13},{8,9,13}}
 # of antimorphisms of SASC-graph: 8 (fair: 2) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,13},
 {3,6,9},{3,8,11},{3,12,13},{4,7,13},{4,9,11},{4,10,12},{5,7,10},{5,8,12},
 {5,9,13},{6,7,12},{6,8,13},{6,10,11}}
 I={{0,13},{1,12},{2,6},{3,10},{4,5},{7,11},{8,9}}
 Examples of antimorphisms:
   A: \alpha=(0 2 6 7 5 4 13 9 8 11 1 12)(3 10)
      B_1={{0,3,4},{0,11,12},{1,3,5},{1,7,9},{2,3,7},{2,4,8},
      {2,5,11},{2,9,12},{3,6,9},{3,8,11},{3,12,13},{4,7,13},
      {4,9,11},{6,7,12}}
   B: \alpha=(0 7 13 11)(1 9 5 2)(3)(4 6 12 8)(10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,3,5},{1,4,6},
      {1,8,10},{1,11,13},{3,12,13},{5,7,10},{5,8,12},{5,9,13},
      {6,8,13},{6,10,11}}
   C: \alpha=(0 4 1 7 8 2 13 12 5 11 6 9)(3 10)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{1,4,6},{1,8,10},
      {1,11,13},{2,10,13},{4,10,12},{5,7,10},{5,8,12},{5,9,13},
      {6,8,13},{6,10,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 46 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,0},{2,9,12},{2,10,13},{3,6,9},{3,8,13},{3,10,12},{3,11,0},
 {4,5,10},{4,7,11},{4,9,0},{4,12,13},{5,7,12},{5,8,0},{5,9,13},{6,7,13},
 {6,8,12},{6,10,11},{7,10,0},{8,9,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 1 7 11)(2 12 13 10 3 8 9 4)(5)(6)
      B_1={{1,4,6},{1,8,10},{1,12,0},{2,4,8},{3,10,12},{4,5,10},
      {4,7,11},{4,12,13},{5,7,12},{5,8,0},{6,8,12},{6,10,11},
      {7,10,0},{8,9,11}}
   B: \alpha=(0 13)(1 3 2 4)(5 6)(7 8)(9 10)(11)(12)
      B_1={{1,3,5},{1,8,10},{1,11,13},{2,4,8},{2,5,11},{2,10,13},
      {3,8,13},{3,10,12},{4,5,10},{4,12,13},{5,7,12},{5,8,0},
      {5,9,13},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,1},{2,9,12},{2,10,13},{3,6,9},{3,8,13},{3,10,12},{3,11,1},
 {4,5,10},{4,7,11},{4,9,1},{4,12,13},{5,7,12},{5,8,1},{5,9,13},{6,7,13},
 {6,8,12},{6,10,11},{7,10,1},{8,9,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,13},{3,10,12},{3,11,2},
 {4,5,10},{4,7,11},{4,9,2},{4,12,13},{5,7,12},{5,8,2},{5,9,13},{6,7,13},
 {6,8,12},{6,10,11},{7,10,2},{8,9,11}}
 I={{0,1},{3,7},{4,8},{5,11},{6,2},{9,12},{10,13}}
 Examples of antimorphisms:
   C: \alpha=(0 5 10 7)(1 8 6 3)(2 11 13 4)(9 12)
      B_1={{0,7,8},{0,11,12},{1,3,5},{1,12,2},{3,8,13},{3,10,12},
      {3,11,2},{4,5,10},{4,7,11},{4,12,13},{5,7,12},{5,8,2},
      {6,7,13},{6,8,12}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,3},{2,9,12},{2,10,13},
 {4,5,10},{4,7,11},{4,9,3},{4,12,13},{5,7,12},{5,8,3},{5,9,13},{6,7,13},
 {6,8,12},{6,10,11},{7,10,3},{8,9,11}}
 I={{0,4},{1,5},{2,7},{6,9},{8,13},{10,12},{11,3}}
 Examples of antimorphisms:
   B: \alpha=(0 1 7 6)(2 9 4 5)(3 10 11 12)(8 13)
      B_1={{0,1,2},{0,11,12},{0,13,3},{1,4,6},{1,11,13},{2,4,8},
      {2,5,11},{2,6,3},{2,10,13},{4,7,11},{4,9,3},{4,12,13},
      {6,7,13},{7,10,3}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,9,12},{2,10,13},
 {3,6,9},{3,8,13},{3,10,12},{3,11,4},{5,7,12},{5,8,4},{5,9,13},{6,7,13},
 {6,8,12},{6,10,11},{7,10,4},{8,9,11}}
 I={{0,3},{1,6},{2,8},{5,10},{7,11},{9,4},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,5},{2,9,12},{2,10,13},
 {3,6,9},{3,8,13},{3,10,12},{3,11,5},{4,7,11},{4,9,5},{4,12,13},{6,7,13},
 {6,8,12},{6,10,11},{7,10,5},{8,9,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,12},{8,5},{9,13}}
 Examples of antimorphisms:
   A: \alpha=(0 8 2 13)(1)(3)(4 10)(5 7 11 6 12 9)
      B_1={{0,1,2},{0,3,4},{0,13,5},{1,4,6},{1,7,9},{2,3,7},
      {2,4,8},{3,6,9},{4,7,11},{4,9,5},{4,12,13},{6,7,13},
      {6,8,12},{8,9,11}}
   C: \alpha=(0 8 2 13)(1 3)(4 10)(5 7 11 6 12 9)
      B_1={{0,1,2},{0,3,4},{0,13,5},{1,4,6},{1,7,9},{2,3,7},
      {2,4,8},{3,6,9},{4,7,11},{4,9,5},{4,12,13},{6,7,13},
      {6,8,12},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,13},
 {3,8,13},{3,10,12},{3,11,6},{4,5,10},{4,7,11},{4,9,6},{4,12,13},{5,7,12},
 {5,8,6},{5,9,13},{7,10,6},{8,9,11}}
 I={{0,5},{1,4},{2,6},{3,9},{7,13},{8,12},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 7 10 12)(1)(2 9 5 11 8 6 3 13)(4)
      B_1={{0,9,10},{0,11,12},{0,13,6},{1,7,9},{1,11,13},{1,12,6},
      {2,10,13},{3,11,6},{4,7,11},{4,9,6},{4,12,13},{5,9,13},
      {7,10,6},{8,9,11}}
   B: \alpha=(0)(1 4)(2 6)(3 9)(5)(7 13)(8 12)(10 11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,6},{2,3,7},{2,5,11},{2,9,12},{2,10,13},
      {3,10,12},{5,7,12}}
   C: \alpha=(0 7 10 12)(1 4)(2 9 5 11 8 6 3 13)
      B_1={{0,9,10},{0,11,12},{0,13,6},{1,7,9},{1,11,13},{1,12,6},
      {2,10,13},{3,11,6},{4,7,11},{4,9,6},{4,12,13},{5,9,13},
      {7,10,6},{8,9,11}}
 # of antimorphisms of SASC-graph: 5 (fair: 1) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,7},{2,9,12},{2,10,13},
 {3,6,9},{3,8,13},{3,10,12},{3,11,7},{4,5,10},{4,9,7},{4,12,13},{5,8,7},
 {5,9,13},{6,8,12},{6,10,11},{8,9,11}}
 I={{0,8},{1,9},{2,3},{4,11},{5,12},{6,13},{10,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,5,11},{2,6,8},{2,9,12},{2,10,13},
 {3,6,9},{3,10,12},{3,11,8},{4,5,10},{4,7,11},{4,9,8},{4,12,13},{5,7,12},
 {5,9,13},{6,7,13},{6,10,11},{7,10,8}}
 I={{0,7},{1,10},{2,4},{3,13},{5,8},{6,12},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,9},{2,10,13},
 {3,8,13},{3,10,12},{3,11,9},{4,5,10},{4,7,11},{4,12,13},{5,7,12},{5,8,9},
 {6,7,13},{6,8,12},{6,10,11},{7,10,9}}
 I={{0,10},{1,7},{2,12},{3,6},{4,9},{5,13},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,8},{2,5,11},{2,6,10},{2,9,12},
 {3,6,9},{3,8,13},{3,11,10},{4,7,11},{4,9,10},{4,12,13},{5,7,12},{5,8,10},
 {5,9,13},{6,7,13},{6,8,12},{8,9,11}}
 I={{0,9},{1,8},{2,13},{3,12},{4,5},{6,11},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,11},{2,9,12},{2,10,13},
 {3,6,9},{3,8,13},{3,10,12},{4,5,10},{4,9,11},{4,12,13},{5,7,12},{5,8,11},
 {5,9,13},{6,7,13},{6,8,12},{7,10,11}}
 I={{0,12},{1,13},{2,5},{3,11},{4,7},{6,10},{8,9}}
 Examples of antimorphisms:
   A: \alpha=(0 6 3 2 12 4 7 5 10 11 9 8)(1 13)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{1,8,10},{1,12,11},{2,9,12},{3,6,9},{3,10,12},
      {5,7,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,12},{2,10,13},
 {3,6,9},{3,8,13},{3,11,12},{4,5,10},{4,7,11},{4,9,12},{5,8,12},{5,9,13},
 {6,7,13},{6,10,11},{7,10,12},{8,9,11}}
 I={{0,11},{1,12},{2,9},{3,10},{4,13},{5,7},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,9,12},
 {3,6,9},{3,10,12},{3,11,13},{4,5,10},{4,7,11},{4,9,13},{5,7,12},{5,8,13},
 {6,8,12},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,13},{1,11},{2,10},{3,8},{4,12},{5,9},{6,7}}
 Examples of antimorphisms:
   C: \alpha=(0 13)(1 6 3 7 11 8)(2 4 9 10 12 5)
      B_1={{1,4,6},{1,7,9},{1,12,13},{2,3,7},{2,5,11},{2,6,13},
      {3,10,12},{3,11,13},{4,5,10},{4,9,13},{5,8,13},{6,8,12},
      {7,10,13},{8,9,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,9,12},{2,10,13},
 {3,6,9},{3,8,13},{3,10,12},{4,5,10},{4,7,11},{4,12,13},{5,7,12},{5,9,13},
 {6,7,13},{6,8,12},{6,10,11},{8,9,11}}
 I={{0,13},{1,12},{2,6},{3,11},{4,9},{5,8},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 47 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,11},{2,6,0},{2,9,13},{2,10,12},{3,6,9},{3,8,12},{3,10,13},{3,11,0},
 {4,5,10},{4,7,11},{4,9,0},{4,12,13},{5,7,13},{5,8,0},{5,9,12},{6,7,12},
 {6,8,13},{6,10,11},{7,10,0},{8,9,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 2)(3 6 11 8)(4 5 12 7)(9 10)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},
      {3,8,12},{3,10,13},{3,11,0},{4,7,11},{4,9,0},{4,12,13},
      {5,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 14 (fair: 14) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,11},{2,6,1},{2,9,13},{2,10,12},{3,6,9},{3,8,12},{3,10,13},{3,11,1},
 {4,5,10},{4,7,11},{4,9,1},{4,12,13},{5,7,13},{5,8,1},{5,9,12},{6,7,12},
 {6,8,13},{6,10,11},{7,10,1},{8,9,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,12},{3,10,13},{3,11,2},
 {4,5,10},{4,7,11},{4,9,2},{4,12,13},{5,7,13},{5,8,2},{5,9,12},{6,7,12},
 {6,8,13},{6,10,11},{7,10,2},{8,9,11}}
 I={{0,1},{3,7},{4,8},{5,11},{6,2},{9,13},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,8},{2,5,11},{2,6,3},{2,9,13},{2,10,12},
 {4,5,10},{4,7,11},{4,9,3},{4,12,13},{5,7,13},{5,8,3},{5,9,12},{6,7,12},
 {6,8,13},{6,10,11},{7,10,3},{8,9,11}}
 I={{0,4},{1,5},{2,7},{6,9},{8,12},{10,13},{11,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,9,13},{2,10,12},
 {3,6,9},{3,8,12},{3,10,13},{3,11,4},{5,7,13},{5,8,4},{5,9,12},{6,7,12},
 {6,8,13},{6,10,11},{7,10,4},{8,9,11}}
 I={{0,3},{1,6},{2,8},{5,10},{7,11},{9,4},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 9 1 13)(2 8)(3 5 12 4 10 6)(7 11)
      B_1={{0,1,2},{0,7,8},{0,13,4},{1,7,9},{1,8,10},{2,3,7},
      {2,10,12},{3,6,9},{3,8,12},{3,10,13},{5,7,13},{5,9,12},
      {6,7,12},{7,10,4}}
   C: \alpha=(0 9 1 13)(2)(3 5 12 4 10 6)(7 11)(8)
      B_1={{0,7,8},{0,13,4},{1,7,9},{1,8,10},{2,3,7},{2,9,13},
      {2,10,12},{3,6,9},{3,8,12},{3,10,13},{5,7,13},{5,9,12},
      {6,7,12},{7,10,4}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,8},{2,6,5},{2,9,13},{2,10,12},
 {3,6,9},{3,8,12},{3,10,13},{3,11,5},{4,7,11},{4,9,5},{4,12,13},{6,7,12},
 {6,8,13},{6,10,11},{7,10,5},{8,9,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,13},{8,5},{9,12}}
 Examples of antimorphisms:
   C: \alpha=(0 5 2 7)(1 13 6 10)(3 8 11 4)(9 12)
      B_1={{0,11,12},{0,13,5},{1,4,6},{1,8,10},{1,12,5},{2,3,7},
      {2,10,12},{3,8,12},{3,11,5},{4,7,11},{4,12,13},{6,7,12},
      {6,8,13},{7,10,5}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,8},{2,5,11},{2,9,13},{2,10,12},
 {3,8,12},{3,10,13},{3,11,6},{4,5,10},{4,7,11},{4,9,6},{4,12,13},{5,7,13},
 {5,8,6},{5,9,12},{7,10,6},{8,9,11}}
 I={{0,5},{1,4},{2,6},{3,9},{7,12},{8,13},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 7 10 13)(1)(2 9 5 11 8 6 3 12)(4)
      B_1={{0,9,10},{0,11,12},{0,13,6},{1,7,9},{1,11,13},{1,12,6},
      {2,10,12},{3,11,6},{4,7,11},{4,9,6},{4,12,13},{5,9,12},
      {7,10,6},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,8},{2,5,11},{2,6,7},{2,9,13},{2,10,12},
 {3,6,9},{3,8,12},{3,10,13},{3,11,7},{4,5,10},{4,9,7},{4,12,13},{5,8,7},
 {5,9,12},{6,8,13},{6,10,11},{8,9,11}}
 I={{0,8},{1,9},{2,3},{4,11},{5,13},{6,12},{10,7}}
 Examples of antimorphisms:
   B: \alpha=(0 6 8 12)(1)(2 4 13 7)(3 11 5 10)(9)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,7},{1,8,10},{1,11,13},
      {2,4,8},{2,5,11},{2,9,13},{2,10,12},{3,10,13},{6,8,13},
      {6,10,11},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,5,11},{2,6,8},{2,9,13},{2,10,12},
 {3,6,9},{3,10,13},{3,11,8},{4,5,10},{4,7,11},{4,9,8},{4,12,13},{5,7,13},
 {5,9,12},{6,7,12},{6,10,11},{7,10,8}}
 I={{0,7},{1,10},{2,4},{3,12},{5,8},{6,13},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,8},{2,5,11},{2,6,9},{2,10,12},
 {3,8,12},{3,10,13},{3,11,9},{4,5,10},{4,7,11},{4,12,13},{5,7,13},{5,8,9},
 {6,7,12},{6,8,13},{6,10,11},{7,10,9}}
 I={{0,10},{1,7},{2,13},{3,6},{4,9},{5,12},{8,11}}
 Examples of antimorphisms:
   A: \alpha=(0 2 3 6 9 11 8 13 5 12 4 10)(1 7)
      B_1={{0,1,2},{0,11,12},{1,3,5},{1,4,6},{1,8,10},{1,11,13},
      {1,12,9},{2,5,11},{2,6,9},{2,10,12},{3,10,13},{4,12,13},
      {6,8,13},{6,10,11}}
   B: \alpha=(0 6 8 12)(1)(2 4 13 9)(3 11 5 10)(7)
      B_1={{0,1,2},{0,7,8},{0,11,12},{0,13,9},{1,8,10},{1,11,13},
      {2,3,7},{2,4,8},{2,5,11},{2,10,12},{3,10,13},{5,7,13},
      {6,8,13},{6,10,11}}
 # of antimorphisms of SASC-graph: 10 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,8},{2,5,11},{2,6,10},{2,9,13},
 {3,6,9},{3,8,12},{3,11,10},{4,7,11},{4,9,10},{4,12,13},{5,7,13},{5,8,10},
 {5,9,12},{6,7,12},{6,8,13},{8,9,11}}
 I={{0,9},{1,8},{2,12},{3,13},{4,5},{6,11},{7,10}}
 Examples of antimorphisms:
   C: \alpha=(0 3 10 1 2 7)(4 11 12 8)(5 6 9 13)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{2,4,8},
      {2,5,11},{2,6,10},{2,9,13},{3,11,10},{4,9,10},{5,8,10},
      {5,9,12},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,8},{2,6,11},{2,9,13},{2,10,12},
 {3,6,9},{3,8,12},{3,10,13},{4,5,10},{4,9,11},{4,12,13},{5,7,13},{5,8,11},
 {5,9,12},{6,7,12},{6,8,13},{7,10,11}}
 I={{0,12},{1,13},{2,5},{3,11},{4,7},{6,10},{8,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,6,12},{2,9,13},
 {3,6,9},{3,10,13},{3,11,12},{4,5,10},{4,7,11},{4,9,12},{5,7,13},{5,8,12},
 {6,8,13},{6,10,11},{7,10,12},{8,9,11}}
 I={{0,11},{1,12},{2,10},{3,8},{4,13},{5,9},{6,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,8},{2,5,11},{2,6,13},{2,10,12},
 {3,6,9},{3,8,12},{3,11,13},{4,5,10},{4,7,11},{4,9,13},{5,8,13},{5,9,12},
 {6,7,12},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,13},{1,11},{2,9},{3,10},{4,12},{5,7},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,8},{2,5,11},{2,9,13},{2,10,12},
 {3,6,9},{3,8,12},{3,10,13},{4,5,10},{4,7,11},{4,12,13},{5,7,13},{5,9,12},
 {6,7,12},{6,8,13},{6,10,11},{8,9,11}}
 I={{0,13},{1,12},{2,6},{3,11},{4,9},{5,8},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 48 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,9},
 {2,5,11},{2,6,0},{2,8,12},{2,10,13},{3,6,8},{3,9,13},{3,10,12},{3,11,0},
 {4,5,10},{4,7,11},{4,8,0},{4,12,13},{5,7,12},{5,8,13},{5,9,0},{6,7,13},
 {6,9,12},{6,10,11},{7,10,0},{8,9,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 2 4 12)(1 6 9 13)(3 11 5 10)(7 8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,12,0},{2,4,9},
      {2,5,11},{3,9,13},{3,10,12},{4,7,11},{4,8,0},{5,9,0},
      {7,10,0},{8,9,11}}
   C: \alpha=(0 2 4 12)(1 6 9 13)(3 11 5 10)(7)(8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,12,0},{2,3,7},
      {2,4,9},{2,5,11},{2,8,12},{3,9,13},{3,10,12},{5,7,12},
      {5,9,0},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,9},
 {2,5,11},{2,6,1},{2,8,12},{2,10,13},{3,6,8},{3,9,13},{3,10,12},{3,11,1},
 {4,5,10},{4,7,11},{4,8,1},{4,12,13},{5,7,12},{5,8,13},{5,9,1},{6,7,13},
 {6,9,12},{6,10,11},{7,10,1},{8,9,11}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,8},{3,9,13},{3,10,12},{3,11,2},
 {4,5,10},{4,7,11},{4,8,2},{4,12,13},{5,7,12},{5,8,13},{5,9,2},{6,7,13},
 {6,9,12},{6,10,11},{7,10,2},{8,9,11}}
 I={{0,1},{3,7},{4,9},{5,11},{6,2},{8,12},{10,13}}
 Examples of antimorphisms:
   C: \alpha=(0 1)(2 12 11 13)(3 10 6 4)(5 9 7 8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,2},
      {3,6,8},{3,9,13},{3,10,12},{4,12,13},{5,7,12},{5,8,13},
      {6,7,13},{6,9,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,9},{2,5,11},{2,6,3},{2,8,12},{2,10,13},
 {4,5,10},{4,7,11},{4,8,3},{4,12,13},{5,7,12},{5,8,13},{5,9,3},{6,7,13},
 {6,9,12},{6,10,11},{7,10,3},{8,9,11}}
 I={{0,4},{1,5},{2,7},{6,8},{9,13},{10,12},{11,3}}
 Examples of antimorphisms:
   B: \alpha=(0 1 7 6)(2 8 4 5)(3 10 11 12)(9 13)
      B_1={{0,1,2},{0,11,12},{0,13,3},{1,4,6},{1,11,13},{2,4,9},
      {2,5,11},{2,6,3},{2,10,13},{4,7,11},{4,8,3},{4,12,13},
      {6,7,13},{7,10,3}}
   C: \alpha=(0 1 10 11)(2 8 4 5)(3 7 6 12)(9 13)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,13,3},{1,12,3},{2,4,9},
      {2,8,12},{2,10,13},{4,5,10},{4,7,11},{4,12,13},{5,7,12},
      {6,7,13},{6,10,11}}
   D: \alpha=(0 6 7 1)(2 5 4 8)(3 12 11 10)(9 13)
      B_1={{0,1,2},{0,11,12},{0,13,3},{1,4,6},{1,11,13},{2,4,9},
      {2,5,11},{2,6,3},{2,10,13},{4,7,11},{4,8,3},{4,12,13},
      {6,7,13},{7,10,3}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,10,13},
 {3,6,8},{3,9,13},{3,10,12},{3,11,4},{5,7,12},{5,8,13},{5,9,4},{6,7,13},
 {6,9,12},{6,10,11},{7,10,4},{8,9,11}}
 I={{0,3},{1,6},{2,9},{5,10},{7,11},{8,4},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 6 13 8)(1 12 10 11)(2)(3 5 7 4)(9)
      B_1={{0,5,6},{0,13,4},{1,8,10},{1,12,4},{2,5,11},{2,6,4},
      {2,8,12},{3,11,4},{5,7,12},{5,8,13},{5,9,4},{6,9,12},
      {6,10,11},{8,9,11}}
   C: \alpha=(0 6 13 8)(1 12 10 11)(2 9)(3 5 7 4)
      B_1={{0,1,2},{0,5,6},{0,13,4},{1,3,5},{1,8,10},{1,12,4},
      {2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,10,13},{5,8,13},
      {6,10,11},{7,10,4}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,9},{2,6,5},{2,8,12},{2,10,13},
 {3,6,8},{3,9,13},{3,10,12},{3,11,5},{4,7,11},{4,8,5},{4,12,13},{6,7,13},
 {6,9,12},{6,10,11},{7,10,5},{8,9,11}}
 I={{0,6},{1,3},{2,11},{4,10},{7,12},{8,13},{9,5}}
 Examples of antimorphisms:
   C: \alpha=(0 1 7 11)(2 3 5 10 6 9 4 12)(8 13)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,5},{1,7,9},{1,11,13},
      {2,3,7},{2,10,13},{3,9,13},{3,10,12},{4,12,13},{6,7,13},
      {6,9,12},{7,10,5}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,9},{2,5,11},{2,8,12},{2,10,13},
 {3,9,13},{3,10,12},{3,11,6},{4,5,10},{4,7,11},{4,8,6},{4,12,13},{5,7,12},
 {5,8,13},{5,9,6},{7,10,6},{8,9,11}}
 I={{0,5},{1,4},{2,6},{3,8},{7,13},{9,12},{10,11}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 4)(2 6)(3 8)(5)(7 13)(9 12)(10 11)
      B_1={{0,1,2},{0,7,8},{0,9,10},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,6},{2,3,7},{2,5,11},{2,8,12},{2,10,13},
      {3,10,12},{5,7,12}}
   D: \alpha=(0 8 5 3)(1 4)(2 6)(7 13)(9 12)(10)(11)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,3,5},{1,7,9},{1,8,10},
      {1,11,13},{1,12,6},{2,3,7},{2,5,11},{2,8,12},{2,10,13},
      {3,10,12},{5,7,12}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,9},{2,5,11},{2,6,7},{2,8,12},{2,10,13},
 {3,6,8},{3,9,13},{3,10,12},{3,11,7},{4,5,10},{4,8,7},{4,12,13},{5,8,13},
 {5,9,7},{6,9,12},{6,10,11},{8,9,11}}
 I={{0,8},{1,9},{2,3},{4,11},{5,12},{6,13},{10,7}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 6 9 13)(2 4 12 7)(3 11 5 10)(8)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,8,10},{1,11,13},{1,12,7},
      {2,4,9},{2,5,11},{2,8,12},{2,10,13},{3,10,12},{6,9,12},
      {6,10,11},{8,9,11}}
   D: \alpha=(0)(1 13 9 6)(2 7 12 4)(3 10 5 11)(8)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,8,10},{1,11,13},{1,12,7},
      {2,4,9},{2,5,11},{2,8,12},{2,10,13},{3,10,12},{6,9,12},
      {6,10,11},{8,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,9},{2,5,11},{2,6,8},{2,10,13},
 {3,9,13},{3,10,12},{3,11,8},{4,5,10},{4,7,11},{4,12,13},{5,7,12},{5,9,8},
 {6,7,13},{6,9,12},{6,10,11},{7,10,8}}
 I={{0,7},{1,10},{2,12},{3,6},{4,8},{5,13},{9,11}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 4 2 6 9 8 12 13)(3 10 5 11)(7)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,11,13},{1,12,8},{2,4,9},
      {2,10,13},{3,11,8},{4,5,10},{4,7,11},{6,7,13},{6,9,12},
      {6,10,11},{7,10,8}}
   B: \alpha=(0)(1 6 9 13)(2 4 12 8)(3 11 5 10)(7)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,7,9},{1,11,13},{1,12,8},
      {2,3,7},{2,4,9},{2,5,11},{2,10,13},{3,10,12},{5,7,12},
      {6,9,12},{6,10,11}}
   C: \alpha=(0)(1 6 12 4 9 13 2 8)(3 10 5 11)(7)
      B_1={{0,3,4},{0,5,6},{0,13,8},{1,3,5},{1,4,6},{1,7,9},
      {2,3,7},{2,5,11},{2,6,8},{3,9,13},{3,10,12},{4,12,13},
      {5,7,12},{5,9,8}}
   D: \alpha=(0)(1 13 9 6)(2 8 12 4)(3 10 5 11)(7)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,7,9},{1,11,13},{1,12,8},
      {2,3,7},{2,4,9},{2,5,11},{2,10,13},{3,10,12},{5,7,12},
      {6,9,12},{6,10,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,5,11},{2,6,9},{2,8,12},{2,10,13},
 {3,6,8},{3,10,12},{3,11,9},{4,5,10},{4,7,11},{4,8,9},{4,12,13},{5,7,12},
 {5,8,13},{6,7,13},{6,10,11},{7,10,9}}
 I={{0,10},{1,7},{2,4},{3,13},{5,9},{6,12},{8,11}}
 Examples of antimorphisms:
   C: \alpha=(0 1 3 4 7 5)(2 10 8 6)(9 13 11 12)
      B_1={{0,5,6},{0,11,12},{0,13,9},{1,3,5},{1,4,6},{1,8,10},
      {2,6,9},{3,10,12},{3,11,9},{4,5,10},{4,7,11},{6,7,13},
      {6,10,11},{7,10,9}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,9},{2,5,11},{2,6,10},{2,8,12},
 {3,6,8},{3,9,13},{3,11,10},{4,7,11},{4,8,10},{4,12,13},{5,7,12},{5,8,13},
 {5,9,10},{6,7,13},{6,9,12},{8,9,11}}
 I={{0,9},{1,8},{2,13},{3,12},{4,5},{6,11},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,9},{2,6,11},{2,8,12},{2,10,13},
 {3,6,8},{3,9,13},{3,10,12},{4,5,10},{4,8,11},{4,12,13},{5,7,12},{5,8,13},
 {5,9,11},{6,7,13},{6,9,12},{7,10,11}}
 I={{0,12},{1,13},{2,5},{3,11},{4,7},{6,10},{8,9}}
 Examples of antimorphisms:
   A: \alpha=(0 6 3 2 12 4 7 5 10 11 8 9)(1 13)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{1,3,5},{1,4,6},
      {1,7,9},{1,8,10},{1,12,11},{2,8,12},{3,6,8},{3,10,12},
      {5,7,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,9},{2,5,11},{2,6,12},{2,10,13},
 {3,6,8},{3,9,13},{3,11,12},{4,5,10},{4,7,11},{4,8,12},{5,8,13},{5,9,12},
 {6,7,13},{6,10,11},{7,10,12},{8,9,11}}
 I={{0,11},{1,12},{2,8},{3,10},{4,13},{5,7},{6,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,9},{2,5,11},{2,6,13},{2,8,12},
 {3,6,8},{3,10,12},{3,11,13},{4,5,10},{4,7,11},{4,8,13},{5,7,12},{5,9,13},
 {6,9,12},{6,10,11},{7,10,13},{8,9,11}}
 I={{0,13},{1,11},{2,10},{3,9},{4,12},{5,8},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 3 13 6 9 7)(1 8 4 11 5 12)(2 10)
      B_1={{0,7,8},{0,9,10},{1,3,5},{1,4,6},{1,8,10},{3,6,8},
      {3,10,12},{3,11,13},{4,5,10},{4,7,11},{5,7,12},{6,9,12},
      {6,10,11},{7,10,13}}
   B: \alpha=(0 6 13 7)(1)(2 10)(3 9)(4 12)(5 8)(11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,11,12},{1,3,5},{1,12,13},
      {2,3,7},{2,4,9},{2,5,11},{2,6,13},{2,8,12},{3,6,8},
      {3,11,13},{4,8,13}}
   D: \alpha=(0 6 13 7)(1 11)(2 10)(3 9)(4 12)(5 8)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,11,12},{1,3,5},{1,8,10},
      {1,12,13},{2,3,7},{2,4,9},{2,6,13},{2,8,12},{3,6,8},
      {3,11,13},{4,8,13}}
 # of antimorphisms of SASC-graph: 9 (fair: 7) 
 # of halving permutations: 2 (fair: 2; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,9},{2,5,11},{2,8,12},{2,10,13},
 {3,6,8},{3,9,13},{3,10,12},{4,5,10},{4,7,11},{4,12,13},{5,7,12},{5,8,13},
 {6,7,13},{6,9,12},{6,10,11},{8,9,11}}
 I={{0,13},{1,12},{2,6},{3,11},{4,8},{5,9},{7,10}}
 Examples of antimorphisms:
   C: \alpha=(0 3 2 10)(1 12)(4 7 13 9)(5 8 11 6)
      B_1={{0,9,10},{1,3,5},{1,4,6},{1,8,10},{1,11,13},{2,3,7},
      {3,6,8},{3,9,13},{3,10,12},{4,5,10},{4,7,11},{4,12,13},
      {5,8,13},{6,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 49 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,9},
 {2,5,11},{2,6,0},{2,8,12},{2,10,13},{3,6,13},{3,8,0},{3,9,11},{3,10,12},
 {4,5,12},{4,7,13},{4,8,11},{4,10,0},{5,7,10},{5,8,13},{5,9,0},{6,7,12},
 {6,8,9},{6,10,11},{7,11,0},{9,12,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,9},
 {2,5,11},{2,6,1},{2,8,12},{2,10,13},{3,6,13},{3,8,1},{3,9,11},{3,10,12},
 {4,5,12},{4,7,13},{4,8,11},{4,10,1},{5,7,10},{5,8,13},{5,9,1},{6,7,12},
 {6,8,9},{6,10,11},{7,11,1},{9,12,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,13},{3,8,2},{3,9,11},{3,10,12},
 {4,5,12},{4,7,13},{4,8,11},{4,10,2},{5,7,10},{5,8,13},{5,9,2},{6,7,12},
 {6,8,9},{6,10,11},{7,11,2},{9,12,13}}
 I={{0,1},{3,7},{4,9},{5,11},{6,2},{8,12},{10,13}}
 Examples of antimorphisms:
   C: \alpha=(0 1)(2 12 11 13)(3 10 6 4)(5 9 7 8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,2},
      {3,6,13},{3,10,12},{4,5,12},{4,7,13},{5,7,10},{5,8,13},
      {6,7,12},{9,12,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,9},{2,5,11},{2,6,3},{2,8,12},{2,10,13},
 {4,5,12},{4,7,13},{4,8,11},{4,10,3},{5,7,10},{5,8,13},{5,9,3},{6,7,12},
 {6,8,9},{6,10,11},{7,11,3},{9,12,13}}
 I={{0,4},{1,5},{2,7},{6,13},{8,3},{9,11},{10,12}}
 Examples of antimorphisms:
   C: \alpha=(0 1 10 4 7 9)(2 8 6 5)(3 13 11 12)
      B_1={{0,1,2},{0,11,12},{0,13,3},{1,4,6},{1,7,9},{2,4,9},
      {2,5,11},{2,6,3},{2,10,13},{4,10,3},{6,7,12},{6,8,9},
      {6,10,11},{7,11,3}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,10,13},
 {3,6,13},{3,8,4},{3,9,11},{3,10,12},{5,7,10},{5,8,13},{5,9,4},{6,7,12},
 {6,8,9},{6,10,11},{7,11,4},{9,12,13}}
 I={{0,3},{1,6},{2,9},{5,12},{7,13},{8,11},{10,4}}
 Examples of antimorphisms:
   C: \alpha=(0 3 8 1 6 2 13 12 11 7 5 9)(4 10)
      B_1={{0,1,2},{0,13,4},{1,3,5},{1,7,9},{1,12,4},{2,3,7},
      {2,6,4},{2,8,12},{3,8,4},{3,9,11},{5,9,4},{6,7,12},
      {7,11,4},{9,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,9},{2,6,5},{2,8,12},{2,10,13},
 {3,6,13},{3,8,5},{3,9,11},{3,10,12},{4,7,13},{4,8,11},{4,10,5},{6,7,12},
 {6,8,9},{6,10,11},{7,11,5},{9,12,13}}
 I={{0,6},{1,3},{2,11},{4,12},{7,10},{8,13},{9,5}}
 Examples of antimorphisms:
   A: \alpha=(0 4 6 12 1 13 2 9)(3 5 7 8 11 10)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,13,5},{1,4,6},{1,8,10},
      {1,12,5},{2,6,5},{2,8,12},{2,10,13},{3,8,5},{4,10,5},
      {6,8,9},{6,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,9},{2,5,11},{2,8,12},{2,10,13},
 {3,8,6},{3,9,11},{3,10,12},{4,5,12},{4,7,13},{4,8,11},{4,10,6},{5,7,10},
 {5,8,13},{5,9,6},{7,11,6},{9,12,13}}
 I={{0,5},{1,4},{2,6},{3,13},{7,12},{8,9},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,9},{2,5,11},{2,6,7},{2,8,12},{2,10,13},
 {3,6,13},{3,8,7},{3,9,11},{3,10,12},{4,5,12},{4,8,11},{4,10,7},{5,8,13},
 {5,9,7},{6,8,9},{6,10,11},{9,12,13}}
 I={{0,8},{1,9},{2,3},{4,13},{5,10},{6,12},{11,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,9},{2,5,11},{2,6,8},{2,10,13},
 {3,6,13},{3,9,11},{3,10,12},{4,5,12},{4,7,13},{4,10,8},{5,7,10},{5,9,8},
 {6,7,12},{6,10,11},{7,11,8},{9,12,13}}
 I={{0,7},{1,10},{2,12},{3,8},{4,11},{5,13},{6,9}}
 Examples of antimorphisms:
   C: \alpha=(0 2 13 3)(1 10)(4 8 7 6)(5 9 11 12)
      B_1={{0,1,2},{0,5,6},{0,13,8},{1,3,5},{1,4,6},{1,7,9},
      {1,11,13},{1,12,8},{2,5,11},{2,6,8},{3,6,13},{3,9,11},
      {4,5,12},{7,11,8}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,5,11},{2,6,9},{2,8,12},{2,10,13},
 {3,6,13},{3,8,9},{3,10,12},{4,5,12},{4,7,13},{4,8,11},{4,10,9},{5,7,10},
 {5,8,13},{6,7,12},{6,10,11},{7,11,9}}
 I={{0,10},{1,7},{2,4},{3,11},{5,9},{6,8},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,9},{2,5,11},{2,6,10},{2,8,12},
 {3,6,13},{3,8,10},{3,9,11},{4,5,12},{4,7,13},{4,8,11},{5,8,13},{5,9,10},
 {6,7,12},{6,8,9},{7,11,10},{9,12,13}}
 I={{0,9},{1,8},{2,13},{3,12},{4,10},{5,7},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,9},{2,6,11},{2,8,12},{2,10,13},
 {3,6,13},{3,8,11},{3,10,12},{4,5,12},{4,7,13},{4,10,11},{5,7,10},{5,8,13},
 {5,9,11},{6,7,12},{6,8,9},{9,12,13}}
 I={{0,12},{1,13},{2,5},{3,9},{4,8},{6,10},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,9},{2,5,11},{2,6,12},{2,10,13},
 {3,6,13},{3,8,12},{3,9,11},{4,7,13},{4,8,11},{4,10,12},{5,7,10},{5,8,13},
 {5,9,12},{6,8,9},{6,10,11},{7,11,12}}
 I={{0,11},{1,12},{2,8},{3,10},{4,5},{6,7},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,9},{2,5,11},{2,6,13},{2,8,12},
 {3,8,13},{3,9,11},{3,10,12},{4,5,12},{4,8,11},{4,10,13},{5,7,10},{5,9,13},
 {6,7,12},{6,8,9},{6,10,11},{7,11,13}}
 I={{0,13},{1,11},{2,10},{3,6},{4,7},{5,8},{9,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,9},{2,5,11},{2,8,12},{2,10,13},
 {3,6,13},{3,9,11},{3,10,12},{4,5,12},{4,7,13},{4,8,11},{5,7,10},{5,8,13},
 {6,7,12},{6,8,9},{6,10,11},{9,12,13}}
 I={{0,13},{1,12},{2,6},{3,8},{4,10},{5,9},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 50 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,9},
 {2,5,11},{2,6,0},{2,8,12},{2,10,13},{3,6,8},{3,9,11},{3,10,0},{3,12,13},
 {4,5,0},{4,7,13},{4,8,11},{4,10,12},{5,7,10},{5,8,13},{5,9,12},{6,7,12},
 {6,9,13},{6,10,11},{7,11,0},{8,9,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 13)(1 2)(3 4)(5 6)(7)(8)(9 10)(11 12)
      B_1={{1,3,5},{1,8,10},{1,11,13},{2,3,7},{2,5,11},{2,10,13},
      {3,9,11},{3,10,0},{4,5,0},{4,8,11},{5,7,10},{5,8,13},
      {5,9,12},{7,11,0}}
 # of antimorphisms of SASC-graph: 1 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,9},
 {2,5,11},{2,6,1},{2,8,12},{2,10,13},{3,6,8},{3,9,11},{3,10,1},{3,12,13},
 {4,5,1},{4,7,13},{4,8,11},{4,10,12},{5,7,10},{5,8,13},{5,9,12},{6,7,12},
 {6,9,13},{6,10,11},{7,11,1},{8,9,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 3 12 7)(1 10 11 9 4 13)(2 5 6 8)
      B_1={{0,3,4},{2,3,7},{2,5,11},{3,6,8},{3,9,11},{3,10,1},
      {4,5,1},{4,7,13},{4,8,11},{5,7,10},{5,8,13},{6,7,12},
      {7,11,1},{8,9,1}}
   C: \alpha=(0 3 12 7)(1 9 4 13)(2 11 10 5 6 8)
      B_1={{0,3,4},{2,3,7},{2,5,11},{3,6,8},{3,9,11},{3,10,1},
      {4,5,1},{4,7,13},{4,8,11},{5,7,10},{5,8,13},{6,7,12},
      {7,11,1},{8,9,1}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,8},{3,9,11},{3,10,2},{3,12,13},
 {4,5,2},{4,7,13},{4,8,11},{4,10,12},{5,7,10},{5,8,13},{5,9,12},{6,7,12},
 {6,9,13},{6,10,11},{7,11,2},{8,9,2}}
 I={{0,1},{3,7},{4,9},{5,11},{6,2},{8,12},{10,13}}
 Examples of antimorphisms:
   C: \alpha=(0 1)(2 7 12 9 11 8)(3 4 6 5)(10 13)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{1,7,9},{1,8,10},
      {3,6,8},{3,9,11},{3,10,2},{4,10,12},{5,7,10},{6,7,12},
      {6,10,11},{8,9,2}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,9},{2,5,11},{2,6,3},{2,8,12},{2,10,13},
 {4,5,3},{4,7,13},{4,8,11},{4,10,12},{5,7,10},{5,8,13},{5,9,12},{6,7,12},
 {6,9,13},{6,10,11},{7,11,3},{8,9,3}}
 I={{0,4},{1,5},{2,7},{6,8},{9,11},{10,3},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,10,13},
 {3,6,8},{3,9,11},{3,10,4},{3,12,13},{5,7,10},{5,8,13},{5,9,12},{6,7,12},
 {6,9,13},{6,10,11},{7,11,4},{8,9,4}}
 I={{0,3},{1,6},{2,9},{5,4},{7,13},{8,11},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,9},{2,6,5},{2,8,12},{2,10,13},
 {3,6,8},{3,9,11},{3,10,5},{3,12,13},{4,7,13},{4,8,11},{4,10,12},{6,7,12},
 {6,9,13},{6,10,11},{7,11,5},{8,9,5}}
 I={{0,6},{1,3},{2,11},{4,5},{7,10},{8,13},{9,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,9},{2,5,11},{2,8,12},{2,10,13},
 {3,9,11},{3,10,6},{3,12,13},{4,5,6},{4,7,13},{4,8,11},{4,10,12},{5,7,10},
 {5,8,13},{5,9,12},{7,11,6},{8,9,6}}
 I={{0,5},{1,4},{2,6},{3,8},{7,12},{9,13},{10,11}}
 Examples of antimorphisms:
   C: \alpha=(0 5)(1 3 4)(2 6)(7 13 11 10 9 12)(8)
      B_1={{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
      {1,12,6},{3,9,11},{3,10,6},{4,5,6},{4,7,13},{4,8,11},
      {7,11,6},{8,9,6}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,9},{2,5,11},{2,6,7},{2,8,12},{2,10,13},
 {3,6,8},{3,9,11},{3,10,7},{3,12,13},{4,5,7},{4,8,11},{4,10,12},{5,8,13},
 {5,9,12},{6,9,13},{6,10,11},{8,9,7}}
 I={{0,8},{1,9},{2,3},{4,13},{5,10},{6,12},{11,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,9},{2,5,11},{2,6,8},{2,10,13},
 {3,9,11},{3,10,8},{3,12,13},{4,5,8},{4,7,13},{4,10,12},{5,7,10},{5,9,12},
 {6,7,12},{6,9,13},{6,10,11},{7,11,8}}
 I={{0,7},{1,10},{2,12},{3,6},{4,11},{5,13},{9,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,5,11},{2,6,9},{2,8,12},{2,10,13},
 {3,6,8},{3,10,9},{3,12,13},{4,5,9},{4,7,13},{4,8,11},{4,10,12},{5,7,10},
 {5,8,13},{6,7,12},{6,10,11},{7,11,9}}
 I={{0,10},{1,7},{2,4},{3,11},{5,12},{6,13},{8,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,9},{2,5,11},{2,6,10},{2,8,12},
 {3,6,8},{3,9,11},{3,12,13},{4,5,10},{4,7,13},{4,8,11},{5,8,13},{5,9,12},
 {6,7,12},{6,9,13},{7,11,10},{8,9,10}}
 I={{0,9},{1,8},{2,13},{3,10},{4,12},{5,7},{6,11}}
 Examples of antimorphisms:
   C: \alpha=(0 3 8 10 1 11 2 7)(4 6 9 12 13 5)
      B_1={{0,3,4},{0,13,10},{1,7,9},{1,11,13},{2,3,7},{2,4,9},
      {3,9,11},{3,12,13},{4,5,10},{4,7,13},{4,8,11},{6,9,13},
      {7,11,10},{8,9,10}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,9},{2,6,11},{2,8,12},{2,10,13},
 {3,6,8},{3,10,11},{3,12,13},{4,5,11},{4,7,13},{4,10,12},{5,7,10},{5,8,13},
 {5,9,12},{6,7,12},{6,9,13},{8,9,11}}
 I={{0,12},{1,13},{2,5},{3,9},{4,8},{6,10},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,9},{2,5,11},{2,6,12},{2,10,13},
 {3,6,8},{3,9,11},{3,10,12},{4,5,12},{4,7,13},{4,8,11},{5,7,10},{5,8,13},
 {6,9,13},{6,10,11},{7,11,12},{8,9,12}}
 I={{0,11},{1,12},{2,8},{3,13},{4,10},{5,9},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 1 4 11 12 5 2 6)(3)(7 9 10 8)(13)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,13,12},{2,3,7},
      {2,4,9},{2,6,12},{2,10,13},{3,10,12},{4,5,12},{4,7,13},
      {4,8,11},{8,9,12}}
   B: \alpha=(0 7 12 2)(1 8 11 6)(3 13)(4 10)(5)(9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,13,12},{1,4,6},
      {1,11,13},{3,10,12},{4,5,12},{4,8,11},{5,8,13},{6,9,13},
      {7,11,12},{8,9,12}}
   C: \alpha=(0 1 4 11 12 5 2 6)(3 13)(7 9 10 8)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,13,12},{2,3,7},
      {2,4,9},{2,6,12},{2,10,13},{3,10,12},{4,5,12},{4,7,13},
      {4,8,11},{8,9,12}}
   D: \alpha=(0 2 12 7)(1 6 11 8)(3 13)(4 10)(5)(9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,13,12},{1,4,6},
      {1,11,13},{3,10,12},{4,5,12},{4,8,11},{5,8,13},{6,9,13},
      {7,11,12},{8,9,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,9},{2,5,11},{2,6,13},{2,8,12},
 {3,6,8},{3,9,11},{3,10,13},{4,5,13},{4,8,11},{4,10,12},{5,7,10},{5,9,12},
 {6,7,12},{6,10,11},{7,11,13},{8,9,13}}
 I={{0,13},{1,11},{2,10},{3,12},{4,7},{5,8},{6,9}}
 Examples of antimorphisms:
   A: \alpha=(0 5 9 6 3 13 4 2 10 11)(1 7 12 8)
      B_1={{0,5,6},{0,7,8},{1,7,9},{2,3,7},{2,5,11},{2,6,13},
      {2,8,12},{3,6,8},{4,5,13},{4,8,11},{5,7,10},{6,10,11},
      {7,11,13},{8,9,13}}
   B: \alpha=(0 13)(1 11)(2 10)(3 12)(4)(5 8)(6 9)(7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},
      {1,7,9},{1,8,10},{2,3,7},{2,4,9},{2,8,12},{3,6,8},
      {3,9,11},{4,8,11}}
   C: \alpha=(0 2 5 3 6 7 8 12)(1 11)(4 13 10 9)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,11,12},{2,5,11},{2,6,13},
      {3,6,8},{3,9,11},{4,5,13},{4,8,11},{5,9,12},{6,10,11},
      {7,11,13},{8,9,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,9},{2,5,11},{2,8,12},{2,10,13},
 {3,6,8},{3,9,11},{3,12,13},{4,7,13},{4,8,11},{4,10,12},{5,7,10},{5,8,13},
 {5,9,12},{6,7,12},{6,9,13},{6,10,11}}
 I={{0,13},{1,12},{2,6},{3,10},{4,5},{7,11},{8,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 51 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,0},{2,8,12},{2,9,13},{3,6,9},{3,8,13},{3,10,12},{3,11,0},
 {4,5,8},{4,7,0},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,0},{6,7,12},
 {6,8,11},{6,10,13},{7,10,11},{8,9,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 4 2 11 6 12 13 9)(1 3 7 10 5 8)
      B_1={{1,8,10},{2,3,7},{2,4,10},{2,8,12},{3,6,9},{3,8,13},
      {3,10,12},{3,11,0},{4,9,11},{4,12,13},{5,10,0},{6,8,11},
      {6,10,13},{8,9,0}}
   C: \alpha=(0 4 2 11)(1 3 7 10 5 8)(6 12 13 9)
      B_1={{1,8,10},{2,3,7},{2,4,10},{2,8,12},{3,6,9},{3,8,13},
      {3,10,12},{3,11,0},{4,9,11},{4,12,13},{5,10,0},{6,8,11},
      {6,10,13},{8,9,0}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,1},{2,8,12},{2,9,13},{3,6,9},{3,8,13},{3,10,12},{3,11,1},
 {4,5,8},{4,7,1},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,1},{6,7,12},
 {6,8,11},{6,10,13},{7,10,11},{8,9,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,13},{3,10,12},{3,11,2},
 {4,5,8},{4,7,2},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,2},{6,7,12},
 {6,8,11},{6,10,13},{7,10,11},{8,9,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,2},{8,12},{9,13}}
 Examples of antimorphisms:
   A: \alpha=(0 5 2 8)(1 10 9 12)(3 7)(4 13 11 6)
      B_1={{0,7,8},{0,11,12},{1,8,10},{3,10,12},{4,5,8},{4,7,2},
      {4,12,13},{5,7,13},{5,9,12},{5,10,2},{6,7,12},{6,8,11},
      {6,10,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,10},{2,5,11},{2,6,3},{2,8,12},{2,9,13},
 {4,5,8},{4,7,3},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,3},{6,7,12},
 {6,8,11},{6,10,13},{7,10,11},{8,9,3}}
 I={{0,4},{1,5},{2,7},{6,9},{8,13},{10,12},{11,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,9,13},
 {3,6,9},{3,8,13},{3,10,12},{3,11,4},{5,7,13},{5,9,12},{5,10,4},{6,7,12},
 {6,8,11},{6,10,13},{7,10,11},{8,9,4}}
 I={{0,3},{1,6},{2,10},{5,8},{7,4},{9,11},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 7 1 13)(2)(3 5 12 4 8 6)(9 11)(10)
      B_1={{0,9,10},{0,13,4},{1,7,9},{1,8,10},{2,3,7},{2,8,12},
      {2,9,13},{3,6,9},{3,8,13},{3,10,12},{5,7,13},{5,9,12},
      {6,7,12},{8,9,4}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,6,5},{2,8,12},{2,9,13},
 {3,6,9},{3,8,13},{3,10,12},{3,11,5},{4,7,5},{4,9,11},{4,12,13},{6,7,12},
 {6,8,11},{6,10,13},{7,10,11},{8,9,5}}
 I={{0,6},{1,3},{2,11},{4,8},{7,13},{9,12},{10,5}}
 Examples of antimorphisms:
   A: \alpha=(0 9 1 6 5 11)(2 3 13 4)(7 8 12 10)
      B_1={{0,3,4},{0,9,10},{1,4,6},{1,8,10},{2,4,10},{2,8,12},
      {3,6,9},{3,8,13},{3,11,5},{4,9,11},{6,8,11},{6,10,13},
      {7,10,11},{8,9,5}}
   C: \alpha=(0 8 12 10 7 9)(1 6 5 11)(2 3 13 4)
      B_1={{0,9,10},{1,8,10},{1,11,13},{2,4,10},{2,6,5},{2,8,12},
      {2,9,13},{3,6,9},{3,8,13},{4,9,11},{6,8,11},{6,10,13},
      {7,10,11},{8,9,5}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,8,13},{3,10,12},{3,11,6},{4,5,8},{4,7,6},{4,9,11},{4,12,13},{5,7,13},
 {5,9,12},{5,10,6},{7,10,11},{8,9,6}}
 I={{0,5},{1,4},{2,6},{3,9},{7,12},{8,11},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,10},{2,5,11},{2,6,7},{2,8,12},{2,9,13},
 {3,6,9},{3,8,13},{3,10,12},{3,11,7},{4,5,8},{4,9,11},{4,12,13},{5,9,12},
 {5,10,7},{6,8,11},{6,10,13},{8,9,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,13},{6,12},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 8 7 13 3 11 10 1 5 2 4 9)(6 12)
      B_1={{0,1,2},{0,5,6},{1,4,6},{1,8,10},{1,11,13},{2,5,11},
      {2,6,7},{2,9,13},{3,6,9},{3,8,13},{4,9,11},{6,8,11},
      {6,10,13},{8,9,7}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,10},{2,5,11},{2,6,8},{2,9,13},
 {3,6,9},{3,10,12},{3,11,8},{4,7,8},{4,9,11},{4,12,13},{5,7,13},{5,9,12},
 {5,10,8},{6,7,12},{6,10,13},{7,10,11}}
 I={{0,7},{1,10},{2,12},{3,13},{4,5},{6,11},{9,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,10},{2,5,11},{2,6,9},{2,8,12},
 {3,8,13},{3,10,12},{3,11,9},{4,5,8},{4,7,9},{4,12,13},{5,7,13},{5,10,9},
 {6,7,12},{6,8,11},{6,10,13},{7,10,11}}
 I={{0,10},{1,7},{2,13},{3,6},{4,11},{5,12},{8,9}}
 Examples of antimorphisms:
   A: \alpha=(0 10)(1 6 3 8 4 13 5 12 7 2 9 11)
      B_1={{1,8,10},{1,11,13},{2,4,10},{2,5,11},{2,6,9},{2,8,12},
      {3,8,13},{3,10,12},{4,12,13},{5,10,9},{6,7,12},{6,8,11},
      {6,10,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,9},{3,8,13},{3,11,10},{4,5,8},{4,7,10},{4,9,11},{4,12,13},{5,7,13},
 {5,9,12},{6,7,12},{6,8,11},{8,9,10}}
 I={{0,9},{1,8},{2,4},{3,12},{5,10},{6,13},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,10},{2,6,11},{2,8,12},{2,9,13},
 {3,6,9},{3,8,13},{3,10,12},{4,5,8},{4,7,11},{4,12,13},{5,7,13},{5,9,12},
 {5,10,11},{6,7,12},{6,10,13},{8,9,11}}
 I={{0,12},{1,13},{2,5},{3,11},{4,9},{6,8},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,6,12},{2,9,13},
 {3,6,9},{3,8,13},{3,11,12},{4,5,8},{4,7,12},{4,9,11},{5,7,13},{5,10,12},
 {6,8,11},{6,10,13},{7,10,11},{8,9,12}}
 I={{0,11},{1,12},{2,8},{3,10},{4,13},{5,9},{6,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,8,12},
 {3,6,9},{3,10,12},{3,11,13},{4,5,8},{4,7,13},{4,9,11},{5,9,12},{5,10,13},
 {6,7,12},{6,8,11},{7,10,11},{8,9,13}}
 I={{0,13},{1,11},{2,9},{3,8},{4,12},{5,7},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,6,9},{3,8,13},{3,10,12},{4,5,8},{4,9,11},{4,12,13},{5,7,13},{5,9,12},
 {6,7,12},{6,8,11},{6,10,13},{7,10,11}}
 I={{0,13},{1,12},{2,6},{3,11},{4,7},{5,10},{8,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 52 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,0},{2,8,12},{2,9,13},{3,6,12},{3,8,13},{3,9,0},{3,10,11},
 {4,5,8},{4,7,0},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,0},{6,7,11},
 {6,8,9},{6,10,13},{7,10,12},{8,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,1},{2,8,12},{2,9,13},{3,6,12},{3,8,13},{3,9,1},{3,10,11},
 {4,5,8},{4,7,1},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,1},{6,7,11},
 {6,8,9},{6,10,13},{7,10,12},{8,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   B: \alpha=(0 7 2 9)(1)(3 13 5 11)(4 6)(8 10)(12)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,13,1},{2,3,7},{2,4,10},
      {2,5,11},{2,6,1},{3,6,12},{3,8,13},{4,5,8},{5,9,12},
      {7,10,12},{8,11,1}}
   D: \alpha=(0 11 2 13)(1 12)(3 7 5 9)(4 6)(8)(10)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,13,1},{2,3,7},{2,4,10},
      {2,5,11},{2,6,1},{3,6,12},{3,8,13},{4,5,8},{5,9,12},
      {7,10,12},{8,11,1}}
 # of antimorphisms of SASC-graph: 8 (fair: 8) 
 # of halving permutations: 2 (fair: 2; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,12},{3,8,13},{3,9,2},{3,10,11},
 {4,5,8},{4,7,2},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,2},{6,7,11},
 {6,8,9},{6,10,13},{7,10,12},{8,11,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,2},{8,12},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,10},{2,5,11},{2,6,3},{2,8,12},{2,9,13},
 {4,5,8},{4,7,3},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,3},{6,7,11},
 {6,8,9},{6,10,13},{7,10,12},{8,11,3}}
 I={{0,4},{1,5},{2,7},{6,12},{8,13},{9,3},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,9,13},
 {3,6,12},{3,8,13},{3,9,4},{3,10,11},{5,7,13},{5,9,12},{5,10,4},{6,7,11},
 {6,8,9},{6,10,13},{7,10,12},{8,11,4}}
 I={{0,3},{1,6},{2,10},{5,8},{7,4},{9,11},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 9 3 13 2 7 5 11)(1 6)(4 8 12 10)
      B_1={{0,7,8},{0,11,12},{1,7,9},{1,8,10},{1,11,13},{2,8,12},
      {2,9,13},{3,9,4},{3,10,11},{5,7,13},{5,10,4},{6,7,11},
      {6,8,9},{6,10,13}}
   C: \alpha=(0 9 3 13 2 7 5 11)(1)(4 8 12 10)(6)
      B_1={{0,7,8},{0,11,12},{1,7,9},{1,11,13},{1,12,4},{2,8,12},
      {2,9,13},{3,9,4},{3,10,11},{5,7,13},{5,10,4},{6,7,11},
      {6,8,9},{6,10,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,6,5},{2,8,12},{2,9,13},
 {3,6,12},{3,8,13},{3,9,5},{3,10,11},{4,7,5},{4,9,11},{4,12,13},{6,7,11},
 {6,8,9},{6,10,13},{7,10,12},{8,11,5}}
 I={{0,6},{1,3},{2,11},{4,8},{7,13},{9,12},{10,5}}
 Examples of antimorphisms:
   A: \alpha=(0 6)(1 9 10 13)(2 8 5 7)(3 12 11 4)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},
      {1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,9,13},{3,9,5},
      {3,10,11},{8,11,5}}
   C: \alpha=(0 6)(1 7 13 2 4 8 9 10)(3 12 11 5)
      B_1={{1,4,6},{1,8,10},{2,3,7},{2,6,5},{2,8,12},{2,9,13},
      {3,6,12},{3,10,11},{4,7,5},{6,7,11},{6,8,9},{6,10,13},
      {7,10,12},{8,11,5}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,8,13},{3,9,6},{3,10,11},{4,5,8},{4,7,6},{4,9,11},{4,12,13},{5,7,13},
 {5,9,12},{5,10,6},{7,10,12},{8,11,6}}
 I={{0,5},{1,4},{2,6},{3,12},{7,11},{8,9},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 9 3 13 2 7 5 11)(1 4)(6 8 12 10)
      B_1={{0,7,8},{0,11,12},{1,7,9},{1,11,13},{1,12,6},{2,8,12},
      {2,9,13},{3,9,6},{3,10,11},{4,7,6},{4,9,11},{4,12,13},
      {5,7,13},{5,10,6}}
   C: \alpha=(0 9 3 13 2 7 5 11)(1)(4)(6 8 12 10)
      B_1={{0,7,8},{0,11,12},{1,7,9},{1,11,13},{1,12,6},{2,8,12},
      {2,9,13},{3,9,6},{3,10,11},{4,7,6},{4,9,11},{4,12,13},
      {5,7,13},{5,10,6}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,10},{2,5,11},{2,6,7},{2,8,12},{2,9,13},
 {3,6,12},{3,8,13},{3,9,7},{3,10,11},{4,5,8},{4,9,11},{4,12,13},{5,9,12},
 {5,10,7},{6,8,9},{6,10,13},{8,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,13},{6,11},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 1 4 12)(2 6 10 3 5 8)(7 13 11 9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,13,7},{2,4,10},
      {2,5,11},{2,6,7},{3,10,11},{4,5,8},{4,9,11},{4,12,13},
      {5,10,7},{8,11,7}}
   C: \alpha=(0 1 4 12)(2 6 10 3 7 13 11 9 5 8)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,13,7},{2,4,10},
      {2,5,11},{2,6,7},{3,10,11},{4,5,8},{4,9,11},{4,12,13},
      {5,10,7},{8,11,7}}
 # of antimorphisms of SASC-graph: 10 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,10},{2,5,11},{2,6,8},{2,9,13},
 {3,6,12},{3,9,8},{3,10,11},{4,7,8},{4,9,11},{4,12,13},{5,7,13},{5,9,12},
 {5,10,8},{6,7,11},{6,10,13},{7,10,12}}
 I={{0,7},{1,10},{2,12},{3,13},{4,5},{6,9},{11,8}}
 Examples of antimorphisms:
   A: \alpha=(0 7)(1 5 9 8)(2 13 6 11)(3 10 4 12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},
      {1,12,8},{2,4,10},{2,5,11},{2,6,8},{3,6,12},{5,9,12},
      {5,10,8},{6,10,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,10},{2,5,11},{2,6,9},{2,8,12},
 {3,6,12},{3,8,13},{3,10,11},{4,5,8},{4,7,9},{4,12,13},{5,7,13},{5,10,9},
 {6,7,11},{6,10,13},{7,10,12},{8,11,9}}
 I={{0,10},{1,7},{2,13},{3,9},{4,11},{5,12},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 13)(2 4 8 9)(5 11 7 12 6 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,13,9},{1,3,5},{1,4,6},
      {2,3,7},{2,6,9},{3,6,12},{4,5,8},{4,7,9},{5,7,13},
      {5,10,9},{6,7,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,12},{3,8,13},{3,9,10},{4,5,8},{4,7,10},{4,9,11},{4,12,13},{5,7,13},
 {5,9,12},{6,7,11},{6,8,9},{8,11,10}}
 I={{0,9},{1,8},{2,4},{3,11},{5,10},{6,13},{7,12}}
 Examples of antimorphisms:
   C: \alpha=(0 1 9 5 8 10)(2 3 6 4 11 13)(7 12)
      B_1={{0,7,8},{0,13,10},{1,3,5},{1,4,6},{1,7,9},{1,11,13},
      {2,3,7},{2,5,11},{2,6,10},{3,9,10},{4,5,8},{4,7,10},
      {5,7,13},{6,7,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,10},{2,6,11},{2,8,12},{2,9,13},
 {3,6,12},{3,8,13},{3,9,11},{4,5,8},{4,7,11},{4,12,13},{5,7,13},{5,9,12},
 {5,10,11},{6,8,9},{6,10,13},{7,10,12}}
 I={{0,12},{1,13},{2,5},{3,10},{4,9},{6,7},{8,11}}
 Examples of antimorphisms:
   B: \alpha=(0 3 12 10)(1)(2 5)(4 9)(6 7)(8 11)(13)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,13,11},{1,4,6},{1,12,11},
      {2,3,7},{2,4,10},{2,8,12},{4,5,8},{4,7,11},{4,12,13},
      {5,7,13},{7,10,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,6,12},{2,9,13},
 {3,8,13},{3,9,12},{3,10,11},{4,5,8},{4,7,12},{4,9,11},{5,7,13},{5,10,12},
 {6,7,11},{6,8,9},{6,10,13},{8,11,12}}
 I={{0,11},{1,12},{2,8},{3,6},{4,13},{5,9},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,8,12},
 {3,6,12},{3,9,13},{3,10,11},{4,5,8},{4,7,13},{4,9,11},{5,9,12},{5,10,13},
 {6,7,11},{6,8,9},{7,10,12},{8,11,13}}
 I={{0,13},{1,11},{2,9},{3,8},{4,12},{5,7},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 3 1 2 7 11)(4 5 13 12 8 9)(6 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,4,6},{1,7,9},
      {1,12,13},{2,6,13},{3,6,12},{4,5,8},{4,7,13},{6,7,11},
      {6,8,9},{8,11,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,6,12},{3,8,13},{3,10,11},{4,5,8},{4,9,11},{4,12,13},{5,7,13},{5,9,12},
 {6,7,11},{6,8,9},{6,10,13},{7,10,12}}
 I={{0,13},{1,12},{2,6},{3,9},{4,7},{5,10},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 53 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,0},{2,8,12},{2,9,13},{3,6,11},{3,8,13},{3,9,0},{3,10,12},
 {4,5,8},{4,7,0},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,0},{6,7,12},
 {6,8,9},{6,10,13},{7,10,11},{8,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 4 2 11)(1 3 7 10 5 8)(6 12 13 9)
      B_1={{1,8,10},{2,3,7},{2,4,10},{2,8,12},{3,6,11},{3,8,13},
      {3,9,0},{3,10,12},{4,9,11},{4,12,13},{5,10,0},{6,8,9},
      {6,10,13},{8,11,0}}
   C: \alpha=(0 4 2 11 6 12 13 9)(1 3 7 10 5 8)
      B_1={{1,8,10},{2,3,7},{2,4,10},{2,8,12},{3,6,11},{3,8,13},
      {3,9,0},{3,10,12},{4,9,11},{4,12,13},{5,10,0},{6,8,9},
      {6,10,13},{8,11,0}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,1},{2,8,12},{2,9,13},{3,6,11},{3,8,13},{3,9,1},{3,10,12},
 {4,5,8},{4,7,1},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,1},{6,7,12},
 {6,8,9},{6,10,13},{7,10,11},{8,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,11},{3,8,13},{3,9,2},{3,10,12},
 {4,5,8},{4,7,2},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,2},{6,7,12},
 {6,8,9},{6,10,13},{7,10,11},{8,11,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,2},{8,12},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,10},{2,5,11},{2,6,3},{2,8,12},{2,9,13},
 {4,5,8},{4,7,3},{4,9,11},{4,12,13},{5,7,13},{5,9,12},{5,10,3},{6,7,12},
 {6,8,9},{6,10,13},{7,10,11},{8,11,3}}
 I={{0,4},{1,5},{2,7},{6,11},{8,13},{9,3},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,9,13},
 {3,6,11},{3,8,13},{3,9,4},{3,10,12},{5,7,13},{5,9,12},{5,10,4},{6,7,12},
 {6,8,9},{6,10,13},{7,10,11},{8,11,4}}
 I={{0,3},{1,6},{2,10},{5,8},{7,4},{9,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,6,5},{2,8,12},{2,9,13},
 {3,6,11},{3,8,13},{3,9,5},{3,10,12},{4,7,5},{4,9,11},{4,12,13},{6,7,12},
 {6,8,9},{6,10,13},{7,10,11},{8,11,5}}
 I={{0,6},{1,3},{2,11},{4,8},{7,13},{9,12},{10,5}}
 Examples of antimorphisms:
   A: \alpha=(0 6)(1 7 13 2 4 8 9 10)(3 12 11 5)
      B_1={{1,4,6},{1,8,10},{2,3,7},{2,6,5},{2,8,12},{2,9,13},
      {3,6,11},{3,10,12},{4,7,5},{6,7,12},{6,8,9},{6,10,13},
      {7,10,11},{8,11,5}}
   B: \alpha=(0 7 6 13)(1)(2 11)(3)(4 8)(5 10)(9 12)
      B_1={{0,1,2},{0,3,4},{0,11,12},{0,13,5},{1,4,6},{1,12,5},
      {2,4,10},{2,6,5},{2,8,12},{3,6,11},{3,9,5},{4,7,5},
      {4,12,13},{6,7,12}}
   C: \alpha=(0 9 1 6 5 11)(2 3 13 4)(7 8 12 10)
      B_1={{0,3,4},{0,9,10},{1,4,6},{1,8,10},{2,4,10},{2,8,12},
      {3,6,11},{3,8,13},{3,9,5},{4,9,11},{6,8,9},{6,10,13},
      {7,10,11},{8,11,5}}
 # of antimorphisms of SASC-graph: 8 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,8,13},{3,9,6},{3,10,12},{4,5,8},{4,7,6},{4,9,11},{4,12,13},{5,7,13},
 {5,9,12},{5,10,6},{7,10,11},{8,11,6}}
 I={{0,5},{1,4},{2,6},{3,11},{7,12},{8,9},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,10},{2,5,11},{2,6,7},{2,8,12},{2,9,13},
 {3,6,11},{3,8,13},{3,9,7},{3,10,12},{4,5,8},{4,9,11},{4,12,13},{5,9,12},
 {5,10,7},{6,8,9},{6,10,13},{8,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,13},{6,12},{10,11}}
 Examples of antimorphisms:
   B: \alpha=(0 5 7 11)(1 3 9 2)(4 10 8 13)(6 12)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,7},{1,4,6},{1,11,13},
      {1,12,7},{2,4,10},{3,8,13},{3,9,7},{5,9,12},{5,10,7},
      {6,8,9},{6,10,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,10},{2,5,11},{2,6,8},{2,9,13},
 {3,6,11},{3,9,8},{3,10,12},{4,7,8},{4,9,11},{4,12,13},{5,7,13},{5,9,12},
 {5,10,8},{6,7,12},{6,10,13},{7,10,11}}
 I={{0,7},{1,10},{2,12},{3,13},{4,5},{6,9},{11,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,10},{2,5,11},{2,6,9},{2,8,12},
 {3,6,11},{3,8,13},{3,10,12},{4,5,8},{4,7,9},{4,12,13},{5,7,13},{5,10,9},
 {6,7,12},{6,10,13},{7,10,11},{8,11,9}}
 I={{0,10},{1,7},{2,13},{3,9},{4,11},{5,12},{6,8}}
 Examples of antimorphisms:
   C: \alpha=(0 4 11 10 8 6)(1 7)(2 9 13 5 3 12)
      B_1={{0,5,6},{0,7,8},{0,11,12},{2,3,7},{2,6,9},{3,10,12},
      {4,5,8},{4,7,9},{4,12,13},{5,7,13},{5,10,9},{6,7,12},
      {7,10,11},{8,11,9}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,11},{3,8,13},{3,9,10},{4,5,8},{4,7,10},{4,9,11},{4,12,13},{5,7,13},
 {5,9,12},{6,7,12},{6,8,9},{8,11,10}}
 I={{0,9},{1,8},{2,4},{3,12},{5,10},{6,13},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,10},{2,6,11},{2,8,12},{2,9,13},
 {3,8,13},{3,9,11},{3,10,12},{4,5,8},{4,7,11},{4,12,13},{5,7,13},{5,9,12},
 {5,10,11},{6,7,12},{6,8,9},{6,10,13}}
 I={{0,12},{1,13},{2,5},{3,6},{4,9},{7,10},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,6,12},{2,9,13},
 {3,6,11},{3,8,13},{3,9,12},{4,5,8},{4,7,12},{4,9,11},{5,7,13},{5,10,12},
 {6,8,9},{6,10,13},{7,10,11},{8,11,12}}
 I={{0,11},{1,12},{2,8},{3,10},{4,13},{5,9},{6,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,8,12},
 {3,6,11},{3,9,13},{3,10,12},{4,5,8},{4,7,13},{4,9,11},{5,9,12},{5,10,13},
 {6,7,12},{6,8,9},{7,10,11},{8,11,13}}
 I={{0,13},{1,11},{2,9},{3,8},{4,12},{5,7},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,6,11},{3,8,13},{3,10,12},{4,5,8},{4,9,11},{4,12,13},{5,7,13},{5,9,12},
 {6,7,12},{6,8,9},{6,10,13},{7,10,11}}
 I={{0,13},{1,12},{2,6},{3,9},{4,7},{5,10},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 54 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,0},{2,8,12},{2,9,13},{3,6,11},{3,8,0},{3,9,12},{3,10,13},
 {4,5,9},{4,7,0},{4,8,11},{4,12,13},{5,7,12},{5,8,13},{5,10,0},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{9,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 2 4 12)(1 6 10 13)(3 11 5 9)(7 8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,12,0},{2,3,7},
      {2,4,10},{2,5,11},{2,8,12},{3,9,12},{3,10,13},{5,7,12},
      {5,10,0},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,1},{2,8,12},{2,9,13},{3,6,11},{3,8,1},{3,9,12},{3,10,13},
 {4,5,9},{4,7,1},{4,8,11},{4,12,13},{5,7,12},{5,8,13},{5,10,1},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{9,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,11},{3,8,2},{3,9,12},{3,10,13},
 {4,5,9},{4,7,2},{4,8,11},{4,12,13},{5,7,12},{5,8,13},{5,10,2},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{9,11,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,2},{8,12},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,10},{2,5,11},{2,6,3},{2,8,12},{2,9,13},
 {4,5,9},{4,7,3},{4,8,11},{4,12,13},{5,7,12},{5,8,13},{5,10,3},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{9,11,3}}
 I={{0,4},{1,5},{2,7},{6,11},{8,3},{9,12},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,9,13},
 {3,6,11},{3,8,4},{3,9,12},{3,10,13},{5,7,12},{5,8,13},{5,10,4},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{9,11,4}}
 I={{0,3},{1,6},{2,10},{5,9},{7,4},{8,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,6,5},{2,8,12},{2,9,13},
 {3,6,11},{3,8,5},{3,9,12},{3,10,13},{4,7,5},{4,8,11},{4,12,13},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{9,11,5}}
 I={{0,6},{1,3},{2,11},{4,9},{7,12},{8,13},{10,5}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,8,6},{3,9,12},{3,10,13},{4,5,9},{4,7,6},{4,8,11},{4,12,13},{5,7,12},
 {5,8,13},{5,10,6},{7,10,11},{9,11,6}}
 I={{0,5},{1,4},{2,6},{3,11},{7,13},{8,9},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,10},{2,5,11},{2,6,7},{2,8,12},{2,9,13},
 {3,6,11},{3,8,7},{3,9,12},{3,10,13},{4,5,9},{4,8,11},{4,12,13},{5,8,13},
 {5,10,7},{6,8,9},{6,10,12},{9,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,12},{6,13},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,10},{2,5,11},{2,6,8},{2,9,13},
 {3,6,11},{3,9,12},{3,10,13},{4,5,9},{4,7,8},{4,12,13},{5,7,12},{5,10,8},
 {6,7,13},{6,10,12},{7,10,11},{9,11,8}}
 I={{0,7},{1,10},{2,12},{3,8},{4,11},{5,13},{6,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,10},{2,5,11},{2,6,9},{2,8,12},
 {3,6,11},{3,8,9},{3,10,13},{4,7,9},{4,8,11},{4,12,13},{5,7,12},{5,8,13},
 {5,10,9},{6,7,13},{6,10,12},{7,10,11}}
 I={{0,10},{1,7},{2,13},{3,12},{4,5},{6,8},{11,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,11},{3,8,10},{3,9,12},{4,5,9},{4,7,10},{4,8,11},{4,12,13},{5,7,12},
 {5,8,13},{6,7,13},{6,8,9},{9,11,10}}
 I={{0,9},{1,8},{2,4},{3,13},{5,10},{6,12},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 13 7)(2 11 6 5 3 12)(4 10 9 8)
      B_1={{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,11,13},{1,12,10},
      {2,5,11},{3,9,12},{4,5,9},{4,8,11},{4,12,13},{5,7,12},
      {5,8,13},{9,11,10}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,10},{2,6,11},{2,8,12},{2,9,13},
 {3,8,11},{3,9,12},{3,10,13},{4,5,9},{4,7,11},{4,12,13},{5,7,12},{5,8,13},
 {5,10,11},{6,7,13},{6,8,9},{6,10,12}}
 I={{0,12},{1,13},{2,5},{3,6},{4,8},{7,10},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,6,12},{2,9,13},
 {3,6,11},{3,8,12},{3,10,13},{4,5,9},{4,7,12},{4,8,11},{5,8,13},{5,10,12},
 {6,7,13},{6,8,9},{7,10,11},{9,11,12}}
 I={{0,11},{1,12},{2,8},{3,9},{4,13},{5,7},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,8,12},
 {3,6,11},{3,8,13},{3,9,12},{4,5,9},{4,7,13},{4,8,11},{5,7,12},{5,10,13},
 {6,8,9},{6,10,12},{7,10,11},{9,11,13}}
 I={{0,13},{1,11},{2,9},{3,10},{4,12},{5,8},{6,7}}
 Examples of antimorphisms:
   C: \alpha=(0 3 6 13 7 10)(1 9 4 11 2 12)(5 8)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,4,6},{1,12,13},
      {2,3,7},{2,4,10},{2,5,11},{3,6,11},{4,5,9},{4,7,13},
      {5,7,12},{5,10,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,6,11},{3,9,12},{3,10,13},{4,5,9},{4,8,11},{4,12,13},{5,7,12},{5,8,13},
 {6,7,13},{6,8,9},{6,10,12},{7,10,11}}
 I={{0,13},{1,12},{2,6},{3,8},{4,7},{5,10},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 55 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,0},{2,8,12},{2,9,13},{3,6,8},{3,9,12},{3,10,13},{3,11,0},
 {4,5,9},{4,7,0},{4,8,11},{4,12,13},{5,7,12},{5,8,13},{5,10,0},{6,7,13},
 {6,9,11},{6,10,12},{7,10,11},{8,9,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 2 4 12)(1 6 10 13)(3 11 5 9)(7)(8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,12,0},{2,4,10},
      {2,5,11},{3,9,12},{3,10,13},{4,7,0},{4,8,11},{5,10,0},
      {7,10,11},{8,9,0}}
   C: \alpha=(0 2 4 12)(1 6 10 13)(3 11 5 9)(7 8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,12,0},{2,3,7},
      {2,4,10},{2,5,11},{2,8,12},{3,9,12},{3,10,13},{5,7,12},
      {5,10,0},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,1},{2,8,12},{2,9,13},{3,6,8},{3,9,12},{3,10,13},{3,11,1},
 {4,5,9},{4,7,1},{4,8,11},{4,12,13},{5,7,12},{5,8,13},{5,10,1},{6,7,13},
 {6,9,11},{6,10,12},{7,10,11},{8,9,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,8},{3,9,12},{3,10,13},{3,11,2},
 {4,5,9},{4,7,2},{4,8,11},{4,12,13},{5,7,12},{5,8,13},{5,10,2},{6,7,13},
 {6,9,11},{6,10,12},{7,10,11},{8,9,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,2},{8,12},{9,13}}
 Examples of antimorphisms:
   C: \alpha=(0 10 8 13)(1 5 2 9)(3 7)(4 12 11 6)
      B_1={{0,13,2},{1,7,9},{1,8,10},{1,11,13},{3,10,13},{4,5,9},
      {4,7,2},{4,12,13},{5,7,12},{5,10,2},{6,7,13},{6,9,11},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,10},{2,5,11},{2,6,3},{2,8,12},{2,9,13},
 {4,5,9},{4,7,3},{4,8,11},{4,12,13},{5,7,12},{5,8,13},{5,10,3},{6,7,13},
 {6,9,11},{6,10,12},{7,10,11},{8,9,3}}
 I={{0,4},{1,5},{2,7},{6,8},{9,12},{10,13},{11,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,12},{2,9,13},
 {3,6,8},{3,9,12},{3,10,13},{3,11,4},{5,7,12},{5,8,13},{5,10,4},{6,7,13},
 {6,9,11},{6,10,12},{7,10,11},{8,9,4}}
 I={{0,3},{1,6},{2,10},{5,9},{7,4},{8,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,6,5},{2,8,12},{2,9,13},
 {3,6,8},{3,9,12},{3,10,13},{3,11,5},{4,7,5},{4,8,11},{4,12,13},{6,7,13},
 {6,9,11},{6,10,12},{7,10,11},{8,9,5}}
 I={{0,6},{1,3},{2,11},{4,9},{7,12},{8,13},{10,5}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,9,12},{3,10,13},{3,11,6},{4,5,9},{4,7,6},{4,8,11},{4,12,13},{5,7,12},
 {5,8,13},{5,10,6},{7,10,11},{8,9,6}}
 I={{0,5},{1,4},{2,6},{3,8},{7,13},{9,11},{10,12}}
 Examples of antimorphisms:
   B: \alpha=(0 5)(1 4)(2 6)(3)(7 13)(8)(9 11)(10 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,11,12},{1,11,13},{1,12,6},
      {2,3,7},{2,5,11},{2,8,12},{2,9,13},{3,9,12},{4,8,11},
      {4,12,13},{5,7,12}}
   C: \alpha=(0 5)(1 9 13 12)(2 4 11 3)(6 7 10 8)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},
      {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,9,13},{3,10,13},
      {4,7,6},{4,8,11}}
 # of antimorphisms of SASC-graph: 3 (fair: 1) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,10},{2,5,11},{2,6,7},{2,8,12},{2,9,13},
 {3,6,8},{3,9,12},{3,10,13},{3,11,7},{4,5,9},{4,8,11},{4,12,13},{5,8,13},
 {5,10,7},{6,9,11},{6,10,12},{8,9,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,12},{6,13},{10,11}}
 Examples of antimorphisms:
   C: \alpha=(0 2 7 13 9 4)(1 6 5 3 8 12)(10)(11)
      B_1={{0,1,2},{0,9,10},{0,13,7},{1,3,5},{1,4,6},{1,8,10},
      {1,11,13},{2,5,11},{2,8,12},{4,5,9},{4,8,11},{5,8,13},
      {5,10,7},{8,9,7}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,10},{2,5,11},{2,6,8},{2,9,13},
 {3,9,12},{3,10,13},{3,11,8},{4,5,9},{4,7,8},{4,12,13},{5,7,12},{5,10,8},
 {6,7,13},{6,9,11},{6,10,12},{7,10,11}}
 I={{0,7},{1,10},{2,12},{3,6},{4,11},{5,13},{9,8}}
 Examples of antimorphisms:
   A: \alpha=(0 2 4 9)(1 10)(3 12 11 13)(5 6 8 7)
      B_1={{0,5,6},{0,9,10},{1,3,5},{1,11,13},{1,12,8},{2,3,7},
      {2,4,10},{2,5,11},{2,9,13},{3,9,12},{3,11,8},{4,7,8},
      {5,10,8},{6,9,11}}
   C: \alpha=(0 6 3 9 4 12 5 13 7 2 8 11)(1 10)
      B_1={{0,9,10},{0,11,12},{2,4,10},{2,5,11},{2,6,8},{2,9,13},
      {3,9,12},{3,10,13},{4,12,13},{5,10,8},{6,7,13},{6,9,11},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,10},{2,5,11},{2,6,9},{2,8,12},
 {3,6,8},{3,10,13},{3,11,9},{4,7,9},{4,8,11},{4,12,13},{5,7,12},{5,8,13},
 {5,10,9},{6,7,13},{6,10,12},{7,10,11}}
 I={{0,10},{1,7},{2,13},{3,12},{4,5},{6,11},{8,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,8},{3,9,12},{3,11,10},{4,5,9},{4,7,10},{4,8,11},{4,12,13},{5,7,12},
 {5,8,13},{6,7,13},{6,9,11},{8,9,10}}
 I={{0,9},{1,8},{2,4},{3,13},{5,10},{6,12},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,10},{2,6,11},{2,8,12},{2,9,13},
 {3,6,8},{3,9,12},{3,10,13},{4,5,9},{4,7,11},{4,12,13},{5,7,12},{5,8,13},
 {5,10,11},{6,7,13},{6,10,12},{8,9,11}}
 I={{0,12},{1,13},{2,5},{3,11},{4,8},{6,9},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,6,12},{2,9,13},
 {3,6,8},{3,10,13},{3,11,12},{4,5,9},{4,7,12},{4,8,11},{5,8,13},{5,10,12},
 {6,7,13},{6,9,11},{7,10,11},{8,9,12}}
 I={{0,11},{1,12},{2,8},{3,9},{4,13},{5,7},{6,10}}
 Examples of antimorphisms:
   C: \alpha=(0 4 9 7 5 1 11 10 12 3 13)(2 8)(6)
      B_1={{0,1,2},{0,9,10},{0,13,12},{1,3,5},{1,4,6},{2,3,7},
      {2,4,10},{2,5,11},{2,6,12},{2,9,13},{3,11,12},{4,5,9},
      {6,7,13},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,8,12},
 {3,6,8},{3,9,12},{3,11,13},{4,5,9},{4,7,13},{4,8,11},{5,7,12},{5,10,13},
 {6,9,11},{6,10,12},{7,10,11},{8,9,13}}
 I={{0,13},{1,11},{2,9},{3,10},{4,12},{5,8},{6,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,6,8},{3,9,12},{3,10,13},{4,5,9},{4,8,11},{4,12,13},{5,7,12},{5,8,13},
 {6,7,13},{6,9,11},{6,10,12},{7,10,11}}
 I={{0,13},{1,12},{2,6},{3,11},{4,7},{5,10},{8,9}}
 Examples of antimorphisms:
   A: \alpha=(0 6 11 12 2 9)(1 8 13 3)(4 7)(5 10)
      B_1={{0,3,4},{0,7,8},{0,9,10},{1,8,10},{2,3,7},{2,4,10},
      {2,8,12},{3,6,8},{3,9,12},{3,10,13},{4,8,11},{6,9,11},
      {6,10,12},{7,10,11}}
   C: \alpha=(0 6 11 12 2 9)(1 8 13 3)(4)(5 10)(7)
      B_1={{0,3,4},{0,7,8},{0,9,10},{1,8,10},{2,3,7},{2,4,10},
      {2,8,12},{3,6,8},{3,9,12},{3,10,13},{4,8,11},{6,9,11},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 56 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,0},{2,8,13},{2,9,12},{3,6,13},{3,8,12},{3,9,0},{3,10,11},
 {4,5,8},{4,7,0},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,0},{6,7,11},
 {6,8,9},{6,10,12},{7,10,13},{8,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 3 8 2 4 12)(1 6 10 13)(5 9 7 11)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,12,0},{2,3,7},
      {2,4,10},{2,5,11},{2,9,12},{3,8,12},{3,10,11},{5,7,12},
      {5,10,0},{7,10,13}}
   C: \alpha=(0 2 4 12)(1 6 10 13)(3 9 7 11 5 8)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,12,0},{2,3,7},
      {2,4,10},{2,5,11},{2,9,12},{3,8,12},{3,10,11},{5,7,12},
      {5,10,0},{7,10,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,1},{2,8,13},{2,9,12},{3,6,13},{3,8,12},{3,9,1},{3,10,11},
 {4,5,8},{4,7,1},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,1},{6,7,11},
 {6,8,9},{6,10,12},{7,10,13},{8,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,13},{3,8,12},{3,9,2},{3,10,11},
 {4,5,8},{4,7,2},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,2},{6,7,11},
 {6,8,9},{6,10,12},{7,10,13},{8,11,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,2},{8,13},{9,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,10},{2,5,11},{2,6,3},{2,8,13},{2,9,12},
 {4,5,8},{4,7,3},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,3},{6,7,11},
 {6,8,9},{6,10,12},{7,10,13},{8,11,3}}
 I={{0,4},{1,5},{2,7},{6,13},{8,12},{9,3},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,13},{2,9,12},
 {3,6,13},{3,8,12},{3,9,4},{3,10,11},{5,7,12},{5,9,13},{5,10,4},{6,7,11},
 {6,8,9},{6,10,12},{7,10,13},{8,11,4}}
 I={{0,3},{1,6},{2,10},{5,8},{7,4},{9,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,6,5},{2,8,13},{2,9,12},
 {3,6,13},{3,8,12},{3,9,5},{3,10,11},{4,7,5},{4,9,11},{4,12,13},{6,7,11},
 {6,8,9},{6,10,12},{7,10,13},{8,11,5}}
 I={{0,6},{1,3},{2,11},{4,8},{7,12},{9,13},{10,5}}
 Examples of antimorphisms:
   A: \alpha=(0 2 12 8 11 3)(1 9 6 7 13 4)(5 10)
      B_1={{0,1,2},{0,9,10},{1,4,6},{1,8,10},{1,11,13},{2,3,7},
      {2,4,10},{2,8,13},{3,6,13},{3,8,12},{3,10,11},{6,8,9},
      {6,10,12},{7,10,13}}
   B: \alpha=(0 6)(1 12 10 9)(2 4 11 8)(3 7 5 13)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,12,5},{2,6,5},{2,8,13},
      {2,9,12},{3,6,13},{3,8,12},{3,9,5},{3,10,11},{4,7,5},
      {4,9,11},{6,7,11}}
   C: \alpha=(0 6)(1 9 10 12)(2 8 5 7)(3 13 11 4)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},
      {1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,9,12},{3,9,5},
      {3,10,11},{8,11,5}}
   D: \alpha=(0 6)(1 9 10 12)(2 8 11 4)(3 13 5 7)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,12,5},{2,6,5},{2,8,13},
      {2,9,12},{3,6,13},{3,8,12},{3,9,5},{3,10,11},{4,7,5},
      {4,9,11},{6,7,11}}
 # of antimorphisms of SASC-graph: 8 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,10},{2,5,11},{2,8,13},{2,9,12},
 {3,8,12},{3,9,6},{3,10,11},{4,5,8},{4,7,6},{4,9,11},{4,12,13},{5,7,12},
 {5,9,13},{5,10,6},{7,10,13},{8,11,6}}
 I={{0,5},{1,4},{2,6},{3,13},{7,11},{8,9},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,10},{2,5,11},{2,6,7},{2,8,13},{2,9,12},
 {3,6,13},{3,8,12},{3,9,7},{3,10,11},{4,5,8},{4,9,11},{4,12,13},{5,9,13},
 {5,10,7},{6,8,9},{6,10,12},{8,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,12},{6,11},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 4 2 12 1 5 8 13)(3 7 6 10 9 11)
      B_1={{0,9,10},{0,11,12},{0,13,7},{1,8,10},{1,11,13},{1,12,7},
      {2,4,10},{2,5,11},{2,6,7},{3,10,11},{4,5,8},{4,12,13},
      {5,10,7},{8,11,7}}
   C: \alpha=(0 1 10 11)(2 8 9 13 6 5 3 12)(4 7)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{1,4,6},{2,4,10},
      {2,6,7},{2,8,13},{3,8,12},{3,9,7},{3,10,11},{4,9,11},
      {5,9,13},{6,10,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,10},{2,5,11},{2,6,8},{2,9,12},
 {3,6,13},{3,9,8},{3,10,11},{4,7,8},{4,9,11},{4,12,13},{5,7,12},{5,9,13},
 {5,10,8},{6,7,11},{6,10,12},{7,10,13}}
 I={{0,7},{1,10},{2,13},{3,12},{4,5},{6,9},{11,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,10},{2,5,11},{2,6,9},{2,8,13},
 {3,6,13},{3,8,12},{3,10,11},{4,5,8},{4,7,9},{4,12,13},{5,7,12},{5,10,9},
 {6,7,11},{6,10,12},{7,10,13},{8,11,9}}
 I={{0,10},{1,7},{2,12},{3,9},{4,11},{5,13},{6,8}}
 Examples of antimorphisms:
   A: \alpha=(0 10)(1 6 5 8 7 13)(2 12)(3)(4 11)(9)
      B_1={{1,4,6},{1,8,10},{1,12,9},{2,4,10},{3,6,13},{3,8,12},
      {3,10,11},{4,5,8},{4,7,9},{4,12,13},{5,7,12},{5,10,9},
      {6,10,12},{7,10,13}}
   B: \alpha=(0 10)(1 7)(2 12)(3 9)(4 11)(5 13)(6)(8)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,11,12},{1,3,5},{1,4,6},
      {1,11,13},{1,12,9},{2,5,11},{2,6,9},{2,8,13},{3,10,11},
      {5,10,9},{8,11,9}}
   C: \alpha=(0 8 10)(1 7)(2 12 5 3 9 13)(4 11)(6)
      B_1={{0,3,4},{0,7,8},{0,13,9},{2,3,7},{2,4,10},{3,6,13},
      {3,8,12},{4,5,8},{4,7,9},{4,12,13},{5,7,12},{6,7,11},
      {6,10,12},{7,10,13}}
   D: \alpha=(0 10)(1 6 7 8)(2 12)(3)(4 11)(5 13)(9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},
      {1,3,5},{1,4,6},{1,12,9},{2,3,7},{2,5,11},{4,5,8},
      {4,7,9},{5,7,12}}
 # of antimorphisms of SASC-graph: 7 (fair: 3) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,5,11},{2,6,10},{2,8,13},{2,9,12},
 {3,6,13},{3,8,12},{3,9,10},{4,5,8},{4,7,10},{4,9,11},{4,12,13},{5,7,12},
 {5,9,13},{6,7,11},{6,8,9},{8,11,10}}
 I={{0,9},{1,8},{2,4},{3,11},{5,10},{6,12},{7,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,10},{2,6,11},{2,8,13},{2,9,12},
 {3,6,13},{3,8,12},{3,9,11},{4,5,8},{4,7,11},{4,12,13},{5,7,12},{5,9,13},
 {5,10,11},{6,8,9},{6,10,12},{7,10,13}}
 I={{0,12},{1,13},{2,5},{3,10},{4,9},{6,7},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,6,12},{2,8,13},
 {3,6,13},{3,9,12},{3,10,11},{4,5,8},{4,7,12},{4,9,11},{5,9,13},{5,10,12},
 {6,7,11},{6,8,9},{7,10,13},{8,11,12}}
 I={{0,11},{1,12},{2,9},{3,8},{4,13},{5,7},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,9,12},
 {3,8,12},{3,9,13},{3,10,11},{4,5,8},{4,7,13},{4,9,11},{5,7,12},{5,10,13},
 {6,7,11},{6,8,9},{6,10,12},{8,11,13}}
 I={{0,13},{1,11},{2,8},{3,6},{4,12},{5,9},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,8,13},{2,9,12},
 {3,6,13},{3,8,12},{3,10,11},{4,5,8},{4,9,11},{4,12,13},{5,7,12},{5,9,13},
 {6,7,11},{6,8,9},{6,10,12},{7,10,13}}
 I={{0,13},{1,12},{2,6},{3,9},{4,7},{5,10},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 57 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,0},{2,8,13},{2,9,12},{3,6,9},{3,8,12},{3,10,13},{3,11,0},
 {4,5,8},{4,7,0},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,0},{6,7,13},
 {6,8,11},{6,10,12},{7,10,11},{8,9,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   C: \alpha=(0 1 13)(2)(3 4)(5 9 8 6 10 7)(11 12)
      B_1={{1,4,6},{1,8,10},{1,12,0},{2,4,10},{2,5,11},{2,8,13},
      {4,5,8},{4,7,0},{4,9,11},{4,12,13},{5,9,13},{5,10,0},
      {6,8,11},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,1},{2,8,13},{2,9,12},{3,6,9},{3,8,12},{3,10,13},{3,11,1},
 {4,5,8},{4,7,1},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,1},{6,7,13},
 {6,8,11},{6,10,12},{7,10,11},{8,9,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,9},{3,8,12},{3,10,13},{3,11,2},
 {4,5,8},{4,7,2},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,2},{6,7,13},
 {6,8,11},{6,10,12},{7,10,11},{8,9,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,2},{8,13},{9,12}}
 Examples of antimorphisms:
   A: \alpha=(0 12 4 3 9 13)(1 7 6 5)(2 11 10 8)
      B_1={{0,13,2},{1,3,5},{1,8,10},{1,11,13},{1,12,2},{3,6,9},
      {3,8,12},{3,10,13},{3,11,2},{4,12,13},{5,7,12},{6,7,13},
      {6,8,11},{6,10,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,10},{2,5,11},{2,6,3},{2,8,13},{2,9,12},
 {4,5,8},{4,7,3},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,3},{6,7,13},
 {6,8,11},{6,10,12},{7,10,11},{8,9,3}}
 I={{0,4},{1,5},{2,7},{6,9},{8,12},{10,13},{11,3}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,13},{2,9,12},
 {3,6,9},{3,8,12},{3,10,13},{3,11,4},{5,7,12},{5,9,13},{5,10,4},{6,7,13},
 {6,8,11},{6,10,12},{7,10,11},{8,9,4}}
 I={{0,3},{1,6},{2,10},{5,8},{7,4},{9,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,6,5},{2,8,13},{2,9,12},
 {3,6,9},{3,8,12},{3,10,13},{3,11,5},{4,7,5},{4,9,11},{4,12,13},{6,7,13},
 {6,8,11},{6,10,12},{7,10,11},{8,9,5}}
 I={{0,6},{1,3},{2,11},{4,8},{7,12},{9,13},{10,5}}
 Examples of antimorphisms:
   A: \alpha=(0 8 13 10 7 9)(1 6 5 11)(2 3 12 4)
      B_1={{0,9,10},{1,4,6},{1,8,10},{2,4,10},{2,8,13},{2,9,12},
      {3,6,9},{3,8,12},{3,11,5},{4,9,11},{6,8,11},{6,10,12},
      {7,10,11},{8,9,5}}
   C: \alpha=(0 9 1 6 5 11)(2 3 12 4)(7 8 13 10)
      B_1={{0,3,4},{0,9,10},{1,4,6},{1,8,10},{2,4,10},{2,8,13},
      {3,6,9},{3,8,12},{3,11,5},{4,9,11},{6,8,11},{6,10,12},
      {7,10,11},{8,9,5}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,10},{2,5,11},{2,8,13},{2,9,12},
 {3,8,12},{3,10,13},{3,11,6},{4,5,8},{4,7,6},{4,9,11},{4,12,13},{5,7,12},
 {5,9,13},{5,10,6},{7,10,11},{8,9,6}}
 I={{0,5},{1,4},{2,6},{3,9},{7,13},{8,11},{10,12}}
 Examples of antimorphisms:
   B: \alpha=(0 5)(1 4)(2 6)(3)(7 13)(8 11)(9)(10 12)
      B_1={{0,1,2},{0,3,4},{0,11,12},{1,11,13},{1,12,6},{2,3,7},
      {2,5,11},{2,8,13},{2,9,12},{3,8,12},{4,9,11},{4,12,13},
      {5,7,12},{5,9,13}}
 # of antimorphisms of SASC-graph: 1 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,10},{2,5,11},{2,6,7},{2,8,13},{2,9,12},
 {3,6,9},{3,8,12},{3,10,13},{3,11,7},{4,5,8},{4,9,11},{4,12,13},{5,9,13},
 {5,10,7},{6,8,11},{6,10,12},{8,9,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,12},{6,13},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,10},{2,5,11},{2,6,8},{2,9,12},
 {3,6,9},{3,10,13},{3,11,8},{4,7,8},{4,9,11},{4,12,13},{5,7,12},{5,9,13},
 {5,10,8},{6,7,13},{6,10,12},{7,10,11}}
 I={{0,7},{1,10},{2,13},{3,12},{4,5},{6,11},{9,8}}
 Examples of antimorphisms:
   C: \alpha=(0 1 4 3 10 6)(2 7 11 13 12 5)(8)(9)
      B_1={{0,5,6},{0,13,8},{1,3,5},{1,4,6},{1,7,9},{1,11,13},
      {2,3,7},{3,6,9},{3,10,13},{4,7,8},{5,7,12},{5,9,13},
      {5,10,8},{6,7,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,10},{2,5,11},{2,6,9},{2,8,13},
 {3,8,12},{3,10,13},{3,11,9},{4,5,8},{4,7,9},{4,12,13},{5,7,12},{5,10,9},
 {6,7,13},{6,8,11},{6,10,12},{7,10,11}}
 I={{0,10},{1,7},{2,12},{3,6},{4,11},{5,13},{8,9}}
 Examples of antimorphisms:
   B: \alpha=(0 10)(1 7)(2 12)(3 6)(4)(5 13)(8 9)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},
      {1,3,5},{1,11,13},{2,3,7},{2,6,9},{2,8,13},{3,11,9},
      {4,7,9},{4,12,13}}
 # of antimorphisms of SASC-graph: 1 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,5,11},{2,6,10},{2,8,13},{2,9,12},
 {3,6,9},{3,8,12},{3,11,10},{4,5,8},{4,7,10},{4,9,11},{4,12,13},{5,7,12},
 {5,9,13},{6,7,13},{6,8,11},{8,9,10}}
 I={{0,9},{1,8},{2,4},{3,13},{5,10},{6,12},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,10},{2,6,11},{2,8,13},{2,9,12},
 {3,6,9},{3,8,12},{3,10,13},{4,5,8},{4,7,11},{4,12,13},{5,7,12},{5,9,13},
 {5,10,11},{6,7,13},{6,10,12},{8,9,11}}
 I={{0,12},{1,13},{2,5},{3,11},{4,9},{6,8},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,6,12},{2,8,13},
 {3,6,9},{3,10,13},{3,11,12},{4,5,8},{4,7,12},{4,9,11},{5,9,13},{5,10,12},
 {6,7,13},{6,8,11},{7,10,11},{8,9,12}}
 I={{0,11},{1,12},{2,9},{3,8},{4,13},{5,7},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,9,12},
 {3,6,9},{3,8,12},{3,11,13},{4,5,8},{4,7,13},{4,9,11},{5,7,12},{5,10,13},
 {6,8,11},{6,10,12},{7,10,11},{8,9,13}}
 I={{0,13},{1,11},{2,8},{3,10},{4,12},{5,9},{6,7}}
 Examples of antimorphisms:
   C: \alpha=(0 2 10 11 6 3 1 4)(5 9)(7 8 12 13)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,4,6},{1,7,9},{2,3,7},
      {2,9,12},{3,6,9},{3,8,12},{4,7,13},{4,9,11},{5,7,12},
      {6,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,8,13},{2,9,12},
 {3,6,9},{3,8,12},{3,10,13},{4,5,8},{4,9,11},{4,12,13},{5,7,12},{5,9,13},
 {6,7,13},{6,8,11},{6,10,12},{7,10,11}}
 I={{0,13},{1,12},{2,6},{3,11},{4,7},{5,10},{8,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 58 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,0},{2,8,13},{2,9,12},{3,6,11},{3,8,12},{3,9,0},{3,10,13},
 {4,5,8},{4,7,0},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,0},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{8,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,1},{2,8,13},{2,9,12},{3,6,11},{3,8,12},{3,9,1},{3,10,13},
 {4,5,8},{4,7,1},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,1},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{8,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 4 7 2 6 9)(1 13 12 5 11 3)(8 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,13,1},{2,3,7},{2,8,13},
      {3,6,11},{3,8,12},{4,5,8},{5,7,12},{5,9,13},{6,7,13},
      {6,8,9},{8,11,1}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,11},{3,8,12},{3,9,2},{3,10,13},
 {4,5,8},{4,7,2},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,2},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{8,11,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,2},{8,13},{9,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,10},{2,5,11},{2,6,3},{2,8,13},{2,9,12},
 {4,5,8},{4,7,3},{4,9,11},{4,12,13},{5,7,12},{5,9,13},{5,10,3},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{8,11,3}}
 I={{0,4},{1,5},{2,7},{6,11},{8,12},{9,3},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,4},{2,8,13},{2,9,12},
 {3,6,11},{3,8,12},{3,9,4},{3,10,13},{5,7,12},{5,9,13},{5,10,4},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{8,11,4}}
 I={{0,3},{1,6},{2,10},{5,8},{7,4},{9,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,10},{2,6,5},{2,8,13},{2,9,12},
 {3,6,11},{3,8,12},{3,9,5},{3,10,13},{4,7,5},{4,9,11},{4,12,13},{6,7,13},
 {6,8,9},{6,10,12},{7,10,11},{8,11,5}}
 I={{0,6},{1,3},{2,11},{4,8},{7,12},{9,13},{10,5}}
 Examples of antimorphisms:
   A: \alpha=(0 9 1 6 5 11)(2 3 12 4)(7 8 13 10)
      B_1={{0,3,4},{0,9,10},{1,4,6},{1,8,10},{2,4,10},{2,8,13},
      {3,6,11},{3,8,12},{3,9,5},{4,9,11},{6,8,9},{6,10,12},
      {7,10,11},{8,11,5}}
   C: \alpha=(0 6)(1 7 12 2 4 8 9 10)(3 13 11 5)
      B_1={{1,4,6},{1,8,10},{2,3,7},{2,6,5},{2,8,13},{2,9,12},
      {3,6,11},{3,10,13},{4,7,5},{6,7,13},{6,8,9},{6,10,12},
      {7,10,11},{8,11,5}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,10},{2,5,11},{2,8,13},{2,9,12},
 {3,8,12},{3,9,6},{3,10,13},{4,5,8},{4,7,6},{4,9,11},{4,12,13},{5,7,12},
 {5,9,13},{5,10,6},{7,10,11},{8,11,6}}
 I={{0,5},{1,4},{2,6},{3,11},{7,13},{8,9},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,10},{2,5,11},{2,6,7},{2,8,13},{2,9,12},
 {3,6,11},{3,8,12},{3,9,7},{3,10,13},{4,5,8},{4,9,11},{4,12,13},{5,9,13},
 {5,10,7},{6,8,9},{6,10,12},{8,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,12},{6,13},{10,11}}
 Examples of antimorphisms:
   B: \alpha=(0 5 7 11)(1 3 9 2)(4 10 8 12)(6 13)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,7},{1,4,6},{1,11,13},
      {1,12,7},{2,4,10},{3,8,12},{3,9,7},{5,9,13},{5,10,7},
      {6,8,9},{6,10,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,10},{2,5,11},{2,6,8},{2,9,12},
 {3,6,11},{3,9,8},{3,10,13},{4,7,8},{4,9,11},{4,12,13},{5,7,12},{5,9,13},
 {5,10,8},{6,7,13},{6,10,12},{7,10,11}}
 I={{0,7},{1,10},{2,13},{3,12},{4,5},{6,9},{11,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,10},{2,5,11},{2,6,9},{2,8,13},
 {3,6,11},{3,8,12},{3,10,13},{4,5,8},{4,7,9},{4,12,13},{5,7,12},{5,10,9},
 {6,7,13},{6,10,12},{7,10,11},{8,11,9}}
 I={{0,10},{1,7},{2,12},{3,9},{4,11},{5,13},{6,8}}
 Examples of antimorphisms:
   B: \alpha=(0 10)(1 6 7 8)(2 12)(3)(4 11)(5 13)(9)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},
      {1,3,5},{1,4,6},{1,12,9},{2,3,7},{2,5,11},{4,5,8},
      {4,7,9},{5,7,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,5,11},{2,6,10},{2,8,13},{2,9,12},
 {3,6,11},{3,8,12},{3,9,10},{4,5,8},{4,7,10},{4,9,11},{4,12,13},{5,7,12},
 {5,9,13},{6,7,13},{6,8,9},{8,11,10}}
 I={{0,9},{1,8},{2,4},{3,13},{5,10},{6,12},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,10},{2,6,11},{2,8,13},{2,9,12},
 {3,8,12},{3,9,11},{3,10,13},{4,5,8},{4,7,11},{4,12,13},{5,7,12},{5,9,13},
 {5,10,11},{6,7,13},{6,8,9},{6,10,12}}
 I={{0,12},{1,13},{2,5},{3,6},{4,9},{7,10},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,6,12},{2,8,13},
 {3,6,11},{3,9,12},{3,10,13},{4,5,8},{4,7,12},{4,9,11},{5,9,13},{5,10,12},
 {6,7,13},{6,8,9},{7,10,11},{8,11,12}}
 I={{0,11},{1,12},{2,9},{3,8},{4,13},{5,7},{6,10}}
 Examples of antimorphisms:
   C: \alpha=(0 2 8 5)(1 13 3 12 10 9)(4 6 7 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{1,3,5},{1,4,6},{1,7,9},
      {1,8,10},{2,3,7},{2,4,10},{3,6,11},{3,10,13},{4,5,8},
      {5,10,12},{7,10,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,9,12},
 {3,6,11},{3,8,12},{3,9,13},{4,5,8},{4,7,13},{4,9,11},{5,7,12},{5,10,13},
 {6,8,9},{6,10,12},{7,10,11},{8,11,13}}
 I={{0,13},{1,11},{2,8},{3,10},{4,12},{5,9},{6,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,10},{2,5,11},{2,8,13},{2,9,12},
 {3,6,11},{3,8,12},{3,10,13},{4,5,8},{4,9,11},{4,12,13},{5,7,12},{5,9,13},
 {6,7,13},{6,8,9},{6,10,12},{7,10,11}}
 I={{0,13},{1,12},{2,6},{3,9},{4,7},{5,10},{8,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 59 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=3 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,0},
 {2,5,11},{2,6,10},{2,8,12},{2,9,13},{3,6,12},{3,8,11},{3,9,0},{3,10,13},
 {4,5,13},{4,7,11},{4,8,9},{4,10,12},{5,7,10},{5,8,0},{5,9,12},{6,7,0},
 {6,8,13},{6,9,11},{7,12,13},{10,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=3 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,1},
 {2,5,11},{2,6,10},{2,8,12},{2,9,13},{3,6,12},{3,8,11},{3,9,1},{3,10,13},
 {4,5,13},{4,7,11},{4,8,9},{4,10,12},{5,7,10},{5,8,1},{5,9,12},{6,7,1},
 {6,8,13},{6,9,11},{7,12,13},{10,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=3 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,12},{3,8,11},{3,9,2},{3,10,13},
 {4,5,13},{4,7,11},{4,8,9},{4,10,12},{5,7,10},{5,8,2},{5,9,12},{6,7,2},
 {6,8,13},{6,9,11},{7,12,13},{10,11,2}}
 I={{0,1},{3,7},{4,2},{5,11},{6,10},{8,12},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,3},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {4,5,13},{4,7,11},{4,8,9},{4,10,12},{5,7,10},{5,8,3},{5,9,12},{6,7,3},
 {6,8,13},{6,9,11},{7,12,13},{10,11,3}}
 I={{0,4},{1,5},{2,7},{6,12},{8,11},{9,3},{10,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 11 9 10 8)(2 5 12 6 3 4 13 7)
      B_1={{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,11,13},{1,12,3},
      {2,5,11},{2,6,10},{2,8,12},{2,9,13},{4,5,13},{4,10,12},
      {6,7,3},{10,11,3}}
   C: \alpha=(0)(1 8 13 12)(2 9 5 7 3 10 6 11)(4)
      B_1={{0,7,8},{0,9,10},{0,11,12},{1,7,9},{1,8,10},{1,11,13},
      {2,9,13},{4,7,11},{4,8,9},{4,10,12},{5,7,10},{6,9,11},
      {7,12,13},{10,11,3}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,12},{3,8,11},{3,9,4},{3,10,13},{5,7,10},{5,8,4},{5,9,12},{6,7,4},
 {6,8,13},{6,9,11},{7,12,13},{10,11,4}}
 I={{0,3},{1,6},{2,4},{5,13},{7,11},{8,9},{10,12}}
 Examples of antimorphisms:
   B: \alpha=(0 3)(1 5 6 13)(2 9 7 10)(4 8 11 12)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},
      {1,7,9},{1,11,13},{2,5,11},{2,6,10},{2,8,12},{5,8,4},
      {6,7,4},{7,12,13}}
   C: \alpha=(0 3)(1 2 10 5)(4 12 11 8)(6 7 9 13)
      B_1={{0,7,8},{0,11,12},{0,13,4},{1,3,5},{1,7,9},{2,3,7},
      {2,5,11},{2,6,10},{2,8,12},{3,10,13},{5,8,4},{5,9,12},
      {6,8,13},{7,12,13}}
   D: \alpha=(0 3)(1 13 6 5)(2 10 7 9)(4 12 11 8)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},
      {1,7,9},{1,11,13},{2,5,11},{2,6,10},{2,8,12},{5,8,4},
      {6,7,4},{7,12,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,5},{2,6,10},{2,8,12},{2,9,13},
 {3,6,12},{3,8,11},{3,9,5},{3,10,13},{4,7,11},{4,8,9},{4,10,12},{6,7,5},
 {6,8,13},{6,9,11},{7,12,13},{10,11,5}}
 I={{0,6},{1,3},{2,11},{4,13},{7,10},{8,5},{9,12}}
 Examples of antimorphisms:
   A: \alpha=(0 3 7 1 6 10)(2 12 13 11 9 4)(5 8)
      B_1={{0,1,2},{0,3,4},{0,13,5},{1,7,9},{1,12,5},{2,4,5},
      {2,6,10},{2,9,13},{3,9,5},{3,10,13},{6,7,5},{6,9,11},
      {7,12,13},{10,11,5}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,6},{2,5,11},{2,8,12},{2,9,13},
 {3,8,11},{3,9,6},{3,10,13},{4,5,13},{4,7,11},{4,8,9},{4,10,12},{5,7,10},
 {5,8,6},{5,9,12},{7,12,13},{10,11,6}}
 I={{0,5},{1,4},{2,10},{3,12},{7,6},{8,13},{9,11}}
 Examples of antimorphisms:
   C: \alpha=(0 1 10 13)(2 8 3 6)(4 12 7 5)(9 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{2,3,7},
      {2,4,6},{2,5,11},{3,8,11},{3,10,13},{4,7,11},{4,10,12},
      {5,7,10},{10,11,6}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 60 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,10},{1,11,13},{1,12,0},{2,3,7},{2,4,0},
 {2,5,11},{2,6,10},{2,8,12},{2,9,13},{3,6,13},{3,8,0},{3,10,12},{3,9,11},
 {4,5,12},{4,7,11},{4,8,9},{4,10,13},{5,7,10},{5,8,13},{5,9,0},{6,7,0},
 {6,8,11},{6,9,12},{7,12,13},{10,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,1},
 {2,5,11},{2,6,10},{2,8,12},{2,9,13},{3,6,13},{3,8,1},{3,10,12},{3,9,11},
 {4,5,12},{4,7,11},{4,8,9},{4,10,13},{5,7,10},{5,8,13},{5,9,1},{6,7,1},
 {6,8,11},{6,9,12},{7,12,13},{10,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,10},{11,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{1,12,2},{3,6,13},{3,8,2},{3,10,12},{3,9,11},
 {4,5,12},{4,7,11},{4,8,9},{4,10,13},{5,7,10},{5,8,13},{5,9,2},{6,7,2},
 {6,8,11},{6,9,12},{7,12,13},{10,11,2}}
 I={{0,1},{3,7},{4,2},{5,11},{6,10},{8,12},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,3},{2,4,3},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {4,5,12},{4,7,11},{4,8,9},{4,10,13},{5,7,10},{5,8,13},{5,9,3},{6,7,3},
 {6,8,11},{6,9,12},{7,12,13},{10,11,3}}
 I={{0,4},{1,5},{2,7},{6,13},{8,3},{10,12},{9,11}}
 Examples of antimorphisms:
   C: \alpha=(0 2 11 4 8 12)(1 5 7 9 3 6 13 10)
      B_1={{0,1,2},{1,4,6},{1,12,3},{2,4,3},{2,6,10},{2,8,12},
      {2,9,13},{4,5,12},{4,7,11},{4,10,13},{5,7,10},{5,9,3},
      {6,9,12},{7,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,4},{2,3,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,13},{3,8,4},{3,10,12},{3,9,11},{5,7,10},{5,8,13},{5,9,4},{6,7,4},
 {6,8,11},{6,9,12},{7,12,13},{10,11,4}}
 I={{0,3},{1,6},{2,4},{5,12},{7,11},{8,9},{10,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,10},{1,11,13},{1,12,5},{2,3,7},{2,4,5},{2,6,10},{2,8,12},{2,9,13},
 {3,6,13},{3,8,5},{3,10,12},{3,9,11},{4,7,11},{4,8,9},{4,10,13},{6,7,5},
 {6,8,11},{6,9,12},{7,12,13},{10,11,5}}
 I={{0,6},{1,3},{2,11},{4,12},{7,10},{8,13},{9,5}}
 Examples of antimorphisms:
   C: \alpha=(0)(1 3 5 11 2 8 10 12)(4 13 7 9)(6)
      B_1={{0,3,4},{0,7,8},{0,11,12},{1,11,13},{2,8,12},{3,6,13},
      {3,8,5},{3,10,12},{3,9,11},{4,7,11},{4,8,9},{6,8,11},
      {6,9,12},{7,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,10},{1,11,13},{1,12,6},{2,3,7},{2,4,6},{2,5,11},{2,8,12},{2,9,13},
 {3,8,6},{3,10,12},{3,9,11},{4,5,12},{4,7,11},{4,8,9},{4,10,13},{5,7,10},
 {5,8,13},{5,9,6},{7,12,13},{10,11,6}}
 I={{0,5},{1,4},{2,10},{3,13},{7,6},{8,11},{9,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,7},{2,4,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,13},{3,8,7},{3,10,12},{3,9,11},{4,5,12},{4,8,9},{4,10,13},{5,8,13},
 {5,9,7},{6,8,11},{6,9,12},{10,11,7}}
 I={{0,8},{1,9},{2,3},{4,11},{5,10},{6,7},{12,13}}
 Examples of antimorphisms:
   C: \alpha=(0 4 6 2 11 13)(1 7 8 9 12 3)(5 10)
      B_1={{0,3,4},{0,9,10},{1,8,10},{1,11,13},{1,12,7},{2,4,7},
      {2,6,10},{2,8,12},{2,9,13},{3,6,13},{3,10,12},{4,8,9},
      {4,10,13},{10,11,7}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,8},{2,3,7},{2,4,8},{2,5,11},{2,6,10},{2,9,13},
 {3,6,13},{3,10,12},{3,9,11},{4,5,12},{4,7,11},{4,10,13},{5,7,10},{5,9,8},
 {6,7,8},{6,9,12},{7,12,13},{10,11,8}}
 I={{0,7},{1,10},{2,12},{3,8},{4,9},{5,13},{6,11}}
 Examples of antimorphisms:
   A: \alpha=(0 7 12 8 6 9 4 13)(1 2 3 10 11 5)
      B_1={{0,1,2},{0,5,6},{0,9,10},{2,4,8},{2,5,11},{2,6,10},
      {2,9,13},{3,10,12},{4,5,12},{4,10,13},{5,7,10},{5,9,8},
      {6,7,8},{7,12,13}}
   C: \alpha=(0 1 8 13 11 3)(2 12 5 10 6 9 4 7)
      B_1={{0,1,2},{0,9,10},{0,11,12},{0,13,8},{1,7,9},{2,6,10},
      {3,10,12},{3,9,11},{4,5,12},{4,7,11},{5,9,8},{6,7,8},
      {7,12,13},{10,11,8}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,10},{1,11,13},{1,12,9},{2,3,7},{2,4,9},{2,5,11},{2,6,10},{2,8,12},
 {3,6,13},{3,8,9},{3,10,12},{4,5,12},{4,7,11},{4,10,13},{5,7,10},{5,8,13},
 {6,7,9},{6,8,11},{7,12,13},{10,11,9}}
 I={{0,10},{1,7},{2,13},{3,11},{4,8},{5,9},{6,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,11,13},{1,12,10},{2,3,7},{2,4,10},{2,5,11},{2,8,12},{2,9,13},
 {3,6,13},{3,8,10},{3,9,11},{4,5,12},{4,7,11},{4,8,9},{5,8,13},{5,9,10},
 {6,7,10},{6,8,11},{6,9,12},{7,12,13}}
 I={{0,9},{1,8},{2,6},{3,12},{4,13},{5,7},{11,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,11},{2,3,7},{2,4,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,13},{3,8,11},{3,10,12},{4,5,12},{4,8,9},{4,10,13},{5,7,10},{5,8,13},
 {5,9,11},{6,7,11},{6,9,12},{7,12,13}}
 I={{0,12},{1,13},{2,5},{3,9},{4,7},{6,8},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 6 7 10)(1)(2 3 12 5 9 4 11 8)(13)
      B_1={{0,3,4},{0,5,6},{0,7,8},{1,3,5},{1,4,6},{1,8,10},
      {2,3,7},{3,6,13},{3,8,11},{4,5,12},{4,8,9},{4,10,13},
      {5,7,10},{5,8,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,4,12},{2,5,11},{2,6,10},{2,9,13},
 {3,6,13},{3,8,12},{3,9,11},{4,7,11},{4,8,9},{4,10,13},{5,7,10},{5,8,13},
 {5,9,12},{6,7,12},{6,8,11},{10,11,12}}
 I={{0,11},{1,12},{2,8},{3,10},{4,5},{6,9},{7,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,12,13},{2,3,7},{2,4,13},{2,5,11},{2,6,10},{2,8,12},
 {3,8,13},{3,10,12},{3,9,11},{4,5,12},{4,7,11},{4,8,9},{5,7,10},{5,9,13},
 {6,7,13},{6,8,11},{6,9,12},{10,11,13}}
 I={{0,13},{1,11},{2,9},{3,6},{4,10},{5,8},{7,12}}
 Examples of antimorphisms:
   C: \alpha=(0 8 9 11)(1 10 6 4 3 13 5 2)(7 12)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{1,12,13},{2,4,13},
      {2,6,10},{2,8,12},{3,10,12},{4,5,12},{4,8,9},{5,9,13},
      {6,9,12},{10,11,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,10},{1,11,13},{2,3,7},{2,5,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,13},{3,10,12},{3,9,11},{4,5,12},{4,7,11},{4,8,9},{4,10,13},{5,7,10},
 {5,8,13},{6,8,11},{6,9,12},{7,12,13}}
 I={{0,13},{1,12},{2,4},{3,8},{5,9},{6,7},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 61 
 |Aut(S)|=21 


 Subsystem No. 0 
 |Aut(T)|=3 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,6},{2,4,5},
 {2,7,10},{2,8,0},{2,9,12},{2,11,13},{3,7,11},{3,8,10},{3,9,0},{3,12,13},
 {4,7,0},{4,8,12},{4,9,13},{4,10,11},{5,7,13},{5,8,9},{5,10,12},{5,11,0},
 {6,7,12},{6,8,13},{6,9,11},{6,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0)(1 5 2 6)(3 4)(7 10 12 9 8 11)(13)
      B_1={{1,3,5},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,6},
      {2,7,10},{2,8,0},{2,9,12},{2,11,13},{4,7,0},{4,8,12},
      {4,9,13},{4,10,11}}
   B: \alpha=(0 13)(1 2)(3 5 4 6)(7 8)(9 10)(11)(12)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},
      {5,7,13},{5,8,9},{5,10,12},{5,11,0},{6,7,12},{6,8,13},
      {6,9,11},{6,10,0}}
 # of antimorphisms of SASC-graph: 42 (fair: 6) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,3,6},{2,4,5},{2,8,7},{2,9,12},{2,11,13},
 {3,8,10},{3,9,7},{3,12,13},{4,8,12},{4,9,13},{4,10,11},{5,8,9},{5,10,12},
 {5,11,7},{6,8,13},{6,9,11},{6,10,7}}
 I={{0,8},{1,9},{2,10},{3,11},{4,7},{5,13},{6,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=21 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,6},{2,4,5},{2,7,10},{2,8,11},{2,9,12},
 {3,8,10},{3,9,11},{3,12,13},{4,7,11},{4,8,12},{4,9,13},{5,7,13},{5,8,9},
 {5,10,12},{6,7,12},{6,8,13},{6,10,11}}
 I={{0,12},{1,8},{2,13},{3,7},{4,10},{5,11},{6,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 62 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,10},{2,8,13},{2,9,12},{2,11,0},{3,7,12},{3,8,9},{3,10,0},{3,11,13},
 {4,5,11},{4,8,0},{4,9,13},{4,10,12},{5,7,13},{5,8,12},{5,9,0},{6,7,0},
 {6,8,10},{6,9,11},{6,12,13},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,7,12},{3,8,9},{3,10,2},{3,11,13},
 {4,5,11},{4,8,2},{4,9,13},{4,10,12},{5,7,13},{5,8,12},{5,9,2},{6,7,2},
 {6,8,10},{6,9,11},{6,12,13},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,10},{8,13},{9,12},{11,2}}
 Examples of antimorphisms:
   A: \alpha=(0 8 3 1 6 13)(2 7 9 11 4 12)(5 10)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,2},{1,4,6},{1,10,13},
      {3,7,12},{3,8,9},{3,10,2},{4,10,12},{6,7,2},{6,8,10},
      {6,9,11},{7,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=3 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,7},{2,5,10},{2,8,13},{2,9,12},{2,11,3},
 {4,5,11},{4,8,3},{4,9,13},{4,10,12},{5,7,13},{5,8,12},{5,9,3},{6,7,3},
 {6,8,10},{6,9,11},{6,12,13},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,12},{8,9},{10,3},{11,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,3,6},{2,5,10},{2,8,13},{2,9,12},{2,11,7},
 {3,8,9},{3,10,7},{3,11,13},{4,5,11},{4,8,7},{4,9,13},{4,10,12},{5,8,12},
 {5,9,7},{6,8,10},{6,9,11},{6,12,13}}
 I={{0,8},{1,9},{2,4},{3,12},{5,13},{6,7},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,6},{2,4,7},{2,5,10},{2,9,12},{2,11,8},
 {3,7,12},{3,10,8},{3,11,13},{4,5,11},{4,9,13},{4,10,12},{5,7,13},{5,9,8},
 {6,7,8},{6,9,11},{6,12,13},{7,10,11}}
 I={{0,7},{1,11},{2,13},{3,9},{4,8},{5,12},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,6},{2,4,7},{2,5,10},{2,8,13},{2,11,9},
 {3,7,12},{3,10,9},{3,11,13},{4,5,11},{4,8,9},{4,10,12},{5,7,13},{5,8,12},
 {6,7,9},{6,8,10},{6,12,13},{7,10,11}}
 I={{0,10},{1,7},{2,12},{3,8},{4,13},{5,9},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,6},{2,4,7},{2,5,10},{2,8,13},{2,11,12},
 {3,8,9},{3,10,12},{3,11,13},{4,5,11},{4,8,12},{4,9,13},{5,7,13},{5,9,12},
 {6,7,12},{6,8,10},{6,9,11},{7,10,11}}
 I={{0,11},{1,12},{2,9},{3,7},{4,10},{5,8},{6,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 63 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,10},{2,8,0},{2,9,12},{2,11,13},{3,7,13},{3,8,9},{3,10,12},{3,11,0},
 {4,5,11},{4,8,12},{4,9,13},{4,10,0},{5,7,12},{5,8,13},{5,9,0},{6,7,0},
 {6,8,10},{6,9,11},{6,12,13},{7,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,7,13},{3,8,9},{3,10,12},{3,11,2},
 {4,5,11},{4,8,12},{4,9,13},{4,10,2},{5,7,12},{5,8,13},{5,9,2},{6,7,2},
 {6,8,10},{6,9,11},{6,12,13},{7,10,11}}
 I={{0,1},{3,6},{4,7},{5,10},{8,2},{9,12},{11,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=3 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,7},{2,5,10},{2,8,3},{2,9,12},{2,11,13},
 {4,5,11},{4,8,12},{4,9,13},{4,10,3},{5,7,12},{5,8,13},{5,9,3},{6,7,3},
 {6,8,10},{6,9,11},{6,12,13},{7,10,11}}
 I={{0,4},{1,5},{2,6},{7,13},{8,9},{10,12},{11,3}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 5)(2 6)(3 11)(4)(7 13)(8 9)(10 12)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,7,9},{1,8,11},{1,10,13},
      {2,4,7},{2,5,10},{2,8,3},{2,9,12},{2,11,13},{4,5,11},
      {4,8,12},{7,10,11}}
   C: \alpha=(0 3 9 7)(1 5)(2 4 11 8 13 10 6 12)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,11,12},{2,5,10},{2,9,12},
      {4,5,11},{4,8,12},{4,9,13},{4,10,3},{5,7,12},{5,8,13},
      {5,9,3},{6,8,10}}
 # of antimorphisms of SASC-graph: 9 (fair: 3) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,3,6},{2,5,10},{2,8,7},{2,9,12},{2,11,13},
 {3,8,9},{3,10,12},{3,11,7},{4,5,11},{4,8,12},{4,9,13},{4,10,7},{5,8,13},
 {5,9,7},{6,8,10},{6,9,11},{6,12,13}}
 I={{0,8},{1,9},{2,4},{3,13},{5,12},{6,7},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,6},{2,4,7},{2,5,10},{2,9,12},{2,11,13},
 {3,7,13},{3,10,12},{3,11,8},{4,5,11},{4,9,13},{4,10,8},{5,7,12},{5,9,8},
 {6,7,8},{6,9,11},{6,12,13},{7,10,11}}
 I={{0,7},{1,11},{2,8},{3,9},{4,12},{5,13},{6,10}}
 Examples of antimorphisms:
   A: \alpha=(0 1 5 12)(2 6 7 11)(3 8 4 9 10 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
      {2,3,6},{2,4,7},{2,5,10},{3,7,13},{3,10,12},{4,5,11},
      {4,10,8},{7,10,11}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,6},{2,4,7},{2,5,10},{2,8,9},{2,11,13},
 {3,7,13},{3,10,12},{3,11,9},{4,5,11},{4,8,12},{4,10,9},{5,7,12},{5,8,13},
 {6,7,9},{6,8,10},{6,12,13},{7,10,11}}
 I={{0,10},{1,7},{2,12},{3,8},{4,13},{5,9},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,6},{2,4,7},{2,5,10},{2,8,12},{2,11,13},
 {3,7,13},{3,8,9},{3,11,12},{4,5,11},{4,9,13},{4,10,12},{5,8,13},{5,9,12},
 {6,7,12},{6,8,10},{6,9,11},{7,10,11}}
 I={{0,11},{1,12},{2,9},{3,10},{4,8},{5,7},{6,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 64 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,6},{2,4,7},
 {2,5,12},{2,8,13},{2,9,11},{2,10,0},{3,7,0},{3,8,12},{3,9,13},{3,10,11},
 {4,5,10},{4,8,0},{4,9,12},{4,11,13},{5,7,13},{5,8,9},{5,11,0},{6,7,11},
 {6,8,10},{6,9,0},{6,12,13},{7,10,12}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=3 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,6},{2,4,7},
 {2,5,12},{2,8,13},{2,9,11},{2,10,1},{3,7,1},{3,8,12},{3,9,13},{3,10,11},
 {4,5,10},{4,8,1},{4,9,12},{4,11,13},{5,7,13},{5,8,9},{5,11,1},{6,7,11},
 {6,8,10},{6,9,1},{6,12,13},{7,10,12}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 1 12 3 6 8 13 10 2 11 5 4)(7 9)
      B_1={{0,3,4},{0,7,8},{2,4,7},{2,10,1},{3,7,1},{3,8,12},
      {3,10,11},{4,8,1},{4,11,13},{5,7,13},{5,11,1},{6,7,11},
      {6,8,10},{7,10,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,7,2},{3,8,12},{3,9,13},{3,10,11},
 {4,5,10},{4,8,2},{4,9,12},{4,11,13},{5,7,13},{5,8,9},{5,11,2},{6,7,11},
 {6,8,10},{6,9,2},{6,12,13},{7,10,12}}
 I={{0,1},{3,6},{4,7},{5,12},{8,13},{9,11},{10,2}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,3,6},{2,5,12},{2,8,13},{2,9,11},{2,10,7},
 {3,8,12},{3,9,13},{3,10,11},{4,5,10},{4,8,7},{4,9,12},{4,11,13},{5,8,9},
 {5,11,7},{6,8,10},{6,9,7},{6,12,13}}
 I={{0,8},{1,9},{2,4},{3,7},{5,13},{6,11},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,6},{2,4,7},{2,5,12},{2,9,11},{2,10,8},
 {3,7,8},{3,9,13},{3,10,11},{4,5,10},{4,9,12},{4,11,13},{5,7,13},{5,11,8},
 {6,7,11},{6,9,8},{6,12,13},{7,10,12}}
 I={{0,7},{1,11},{2,13},{3,12},{4,8},{5,9},{6,10}}
 Examples of antimorphisms:
   C: \alpha=(0 3 7)(1 9 10 11 6 5)(2 13)(4 8)(12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{1,7,9},{1,10,13},{1,12,8},
      {2,3,6},{2,4,7},{2,10,8},{3,10,11},{5,11,8},{6,9,8},
      {6,12,13},{7,10,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,6},{2,4,7},{2,5,12},{2,8,13},{2,10,9},
 {3,7,9},{3,8,12},{3,10,11},{4,5,10},{4,8,9},{4,11,13},{5,7,13},{5,11,9},
 {6,7,11},{6,8,10},{6,12,13},{7,10,12}}
 I={{0,10},{1,7},{2,11},{3,13},{4,12},{5,8},{6,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=3 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,6},{2,4,7},{2,5,12},{2,8,13},{2,10,11},
 {3,7,11},{3,8,12},{3,9,13},{4,5,10},{4,8,11},{4,9,12},{5,7,13},{5,8,9},
 {6,8,10},{6,9,11},{6,12,13},{7,10,12}}
 I={{0,12},{1,8},{2,9},{3,10},{4,13},{5,11},{6,7}}
 Examples of antimorphisms:
   A: \alpha=(0 1 3 6 11 10)(2 9)(4)(5 12 7 8)(13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,13,11},{1,3,5},{1,7,9},
      {3,7,11},{3,9,13},{4,8,11},{4,9,12},{5,7,13},{5,8,9},
      {6,9,11},{7,10,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 65 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,13},{2,6,10},{2,9,12},{2,11,0},{3,6,0},{3,8,9},{3,10,11},{3,12,13},
 {4,5,11},{4,7,0},{4,9,13},{4,10,12},{5,7,10},{5,8,12},{5,9,0},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 5 10 11 7 3 12 8)(1 4 13 2 6 9)
      B_1={{1,3,5},{1,4,6},{1,8,11},{1,10,13},{1,12,0},{2,5,13},
      {3,6,0},{3,12,13},{5,7,10},{6,7,12},{6,8,13},{6,9,11},
      {7,11,13},{8,10,0}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,13},{2,6,10},{2,9,12},{2,11,1},{3,6,1},{3,8,9},{3,10,11},{3,12,13},
 {4,5,11},{4,7,1},{4,9,13},{4,10,12},{5,7,10},{5,8,12},{5,9,1},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,11},{3,12,13},
 {4,5,11},{4,7,2},{4,9,13},{4,10,12},{5,7,10},{5,8,12},{5,9,2},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,2}}
 I={{0,1},{3,7},{4,8},{5,13},{6,10},{9,12},{11,2}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,8},{2,5,13},{2,6,10},{2,9,12},{2,11,3},
 {4,5,11},{4,7,3},{4,9,13},{4,10,12},{5,7,10},{5,8,12},{5,9,3},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,9},{10,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,13},{2,6,10},{2,9,12},{2,11,4},
 {3,6,4},{3,8,9},{3,10,11},{3,12,13},{5,7,10},{5,8,12},{5,9,4},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,4}}
 I={{0,3},{1,6},{2,8},{5,11},{7,4},{9,13},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,8},{2,6,10},{2,9,12},{2,11,5},
 {3,6,5},{3,8,9},{3,10,11},{3,12,13},{4,7,5},{4,9,13},{4,10,12},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,5}}
 I={{0,6},{1,3},{2,13},{4,11},{7,10},{8,12},{9,5}}
 Examples of antimorphisms:
   A: \alpha=(0 6)(1 9 8 10)(2 11 12 7)(3 5 13 4)
      B_1={{0,1,2},{0,7,8},{0,11,12},{1,4,6},{1,7,9},{1,8,11},
      {2,3,7},{3,6,5},{3,10,11},{3,12,13},{4,9,13},{6,8,13},
      {7,11,13},{8,10,5}}
   C: \alpha=(0 7 11 12 10 13)(1 5 8 4)(2 6 3 9)
      B_1={{0,13,5},{1,7,9},{1,12,5},{2,3,7},{2,4,8},{2,9,12},
      {3,6,5},{3,12,13},{4,7,5},{4,9,13},{4,10,12},{6,7,12},
      {6,8,13},{7,11,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,6},{2,3,7},{2,4,8},{2,5,13},{2,9,12},{2,11,6},
 {3,8,9},{3,10,11},{3,12,13},{4,5,11},{4,7,6},{4,9,13},{4,10,12},{5,7,10},
 {5,8,12},{5,9,6},{7,11,13},{8,10,6}}
 I={{0,5},{1,4},{2,10},{3,6},{7,12},{8,13},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,8},{2,5,13},{2,6,10},{2,9,12},{2,11,7},
 {3,6,7},{3,8,9},{3,10,11},{3,12,13},{4,5,11},{4,9,13},{4,10,12},{5,8,12},
 {5,9,7},{6,8,13},{6,9,11},{8,10,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,10},{6,12},{11,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,5,13},{2,6,10},{2,9,12},{2,11,8},
 {3,6,8},{3,10,11},{3,12,13},{4,5,11},{4,7,8},{4,9,13},{4,10,12},{5,7,10},
 {5,9,8},{6,7,12},{6,9,11},{7,11,13}}
 I={{0,7},{1,11},{2,4},{3,9},{5,12},{6,13},{10,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,7},{2,4,8},{2,5,13},{2,6,10},{2,11,9},
 {3,6,9},{3,10,11},{3,12,13},{4,5,11},{4,7,9},{4,10,12},{5,7,10},{5,8,12},
 {6,7,12},{6,8,13},{7,11,13},{8,10,9}}
 I={{0,10},{1,7},{2,12},{3,8},{4,13},{5,9},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,7},{2,4,8},{2,5,13},{2,9,12},{2,11,10},
 {3,6,10},{3,8,9},{3,12,13},{4,5,11},{4,7,10},{4,9,13},{5,8,12},{5,9,10},
 {6,7,12},{6,8,13},{6,9,11},{7,11,13}}
 I={{0,9},{1,13},{2,6},{3,11},{4,12},{5,7},{8,10}}
 Examples of antimorphisms:
   A: \alpha=(0 2 12 3)(1 5 6 4 11 9 13 7)(8 10)
      B_1={{0,3,4},{0,7,8},{1,3,5},{1,4,6},{2,3,7},{2,4,8},
      {2,5,13},{2,9,12},{3,8,9},{4,7,10},{5,8,12},{5,9,10},
      {6,9,11},{7,11,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,7},{2,4,8},{2,5,13},{2,6,10},{2,9,12},
 {3,6,11},{3,8,9},{3,12,13},{4,7,11},{4,9,13},{4,10,12},{5,7,10},{5,8,12},
 {5,9,11},{6,7,12},{6,8,13},{8,10,11}}
 I={{0,12},{1,8},{2,11},{3,10},{4,5},{6,9},{7,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,8},{2,5,13},{2,6,10},{2,11,12},
 {3,6,12},{3,8,9},{3,10,11},{4,5,11},{4,7,12},{4,9,13},{5,7,10},{5,9,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,12}}
 I={{0,11},{1,12},{2,9},{3,13},{4,10},{5,8},{6,7}}
 Examples of antimorphisms:
   C: \alpha=(0 4 5 13)(1 7 2 12 3 11)(6 10 8 9)
      B_1={{0,1,2},{0,3,4},{1,3,5},{1,4,6},{1,8,11},{1,10,13},
      {2,3,7},{2,4,8},{2,5,13},{2,6,10},{3,6,12},{3,8,9},
      {4,9,13},{6,8,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,4,8},{2,6,10},{2,9,12},{2,11,13},
 {3,6,13},{3,8,9},{3,10,11},{4,5,11},{4,7,13},{4,10,12},{5,7,10},{5,8,12},
 {5,9,13},{6,7,12},{6,9,11},{8,10,13}}
 I={{0,13},{1,10},{2,5},{3,12},{4,9},{6,8},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 8 3 11)(1 12 7 4)(2)(5)(6 9 10 13)
      B_1={{0,3,4},{0,11,12},{1,7,9},{1,12,13},{2,4,8},{2,9,12},
      {2,11,13},{3,8,9},{4,5,11},{4,7,13},{5,8,12},{5,9,13},
      {6,9,11},{8,10,13}}
   C: \alpha=(0 8 3 11)(1 12 7 4)(2 5)(6 9 10 13)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{1,7,9},{1,12,13},
      {2,3,7},{2,4,8},{2,6,10},{2,9,12},{2,11,13},{3,6,13},
      {3,8,9},{4,7,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,8},{2,5,13},{2,6,10},{2,9,12},
 {3,8,9},{3,10,11},{3,12,13},{4,5,11},{4,9,13},{4,10,12},{5,7,10},{5,8,12},
 {6,7,12},{6,8,13},{6,9,11},{7,11,13}}
 I={{0,13},{1,12},{2,11},{3,6},{4,7},{5,9},{8,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 66 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,11},
 {2,5,13},{2,6,10},{2,8,12},{2,9,0},{3,6,0},{3,8,9},{3,10,11},{3,12,13},
 {4,5,8},{4,7,0},{4,9,13},{4,10,12},{5,7,10},{5,9,12},{5,11,0},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 1 10 11 5 9)(2 12 13 6)(3 4)(7 8)
      B_1={{1,4,6},{1,10,13},{2,4,11},{2,5,13},{2,8,12},{2,9,0},
      {4,5,8},{4,7,0},{4,9,13},{4,10,12},{5,7,10},{5,11,0},
      {6,8,13},{8,10,0}}
   C: \alpha=(0 4 8 2 5 12 1 6)(3 7 10 11 13 9)
      B_1={{1,3,5},{1,10,13},{1,12,0},{2,3,7},{2,5,13},{2,6,10},
      {3,6,0},{3,10,11},{3,12,13},{4,5,8},{4,9,13},{4,10,12},
      {6,8,13},{8,10,0}}
 # of antimorphisms of SASC-graph: 8 (fair: 0) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,11},
 {2,5,13},{2,6,10},{2,8,12},{2,9,1},{3,6,1},{3,8,9},{3,10,11},{3,12,13},
 {4,5,8},{4,7,1},{4,9,13},{4,10,12},{5,7,10},{5,9,12},{5,11,1},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 2)(1 7 6 11)(3 8 10 5 4 12 9 13)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {3,12,13},{4,5,8},{5,9,12},{5,11,1},{6,7,12},{6,8,13},
      {7,11,13},{8,10,1}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,11},{3,12,13},
 {4,5,8},{4,7,2},{4,9,13},{4,10,12},{5,7,10},{5,9,12},{5,11,2},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,2}}
 I={{0,1},{3,7},{4,11},{5,13},{6,10},{8,12},{9,2}}
 Examples of antimorphisms:
   B: \alpha=(0 11 3 8)(1 4 7 12)(2 10 9 6)(5)(13)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,2},{1,7,9},{1,12,2},
      {3,6,2},{3,8,9},{3,12,13},{4,5,8},{4,7,2},{4,9,13},
      {5,9,12},{5,11,2}}
   D: \alpha=(0 8 3 11)(1 12 7 4)(2 6 9 10)(5)(13)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,2},{1,7,9},{1,12,2},
      {3,6,2},{3,8,9},{3,12,13},{4,5,8},{4,7,2},{4,9,13},
      {5,9,12},{5,11,2}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 1 (fair: 1; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,11},{2,5,13},{2,6,10},{2,8,12},{2,9,3},
 {4,5,8},{4,7,3},{4,9,13},{4,10,12},{5,7,10},{5,9,12},{5,11,3},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,9},{10,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,13},{2,6,10},{2,8,12},{2,9,4},
 {3,6,4},{3,8,9},{3,10,11},{3,12,13},{5,7,10},{5,9,12},{5,11,4},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,4}}
 I={{0,3},{1,6},{2,11},{5,8},{7,4},{9,13},{10,12}}
 Examples of antimorphisms:
   A: \alpha=(0 3)(1 9 4 10)(2 8 13 7)(5 12 6 11)
      B_1={{0,9,10},{0,11,12},{1,10,13},{2,3,7},{2,5,13},{2,6,10},
      {2,9,4},{3,8,9},{3,10,11},{3,12,13},{5,7,10},{5,9,12},
      {6,8,13},{6,9,11}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,11},{2,6,10},{2,8,12},{2,9,5},
 {3,6,5},{3,8,9},{3,10,11},{3,12,13},{4,7,5},{4,9,13},{4,10,12},{6,7,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,5}}
 I={{0,6},{1,3},{2,13},{4,8},{7,10},{9,12},{11,5}}
 Examples of antimorphisms:
   C: \alpha=(0 8 3 11)(1 12 7 4)(2)(5 6 9 10)(13)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{0,13,5},{1,7,9},
      {1,12,5},{2,3,7},{2,6,10},{3,6,5},{3,8,9},{3,12,13},
      {4,7,5},{4,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,6},{2,3,7},{2,4,11},{2,5,13},{2,8,12},{2,9,6},
 {3,8,9},{3,10,11},{3,12,13},{4,5,8},{4,7,6},{4,9,13},{4,10,12},{5,7,10},
 {5,9,12},{5,11,6},{7,11,13},{8,10,6}}
 I={{0,5},{1,4},{2,10},{3,6},{7,12},{8,13},{9,11}}
 Examples of antimorphisms:
   A: \alpha=(0 4 11 5 2 6 13 9)(1 8 10 3)(7)(12)
      B_1={{0,1,2},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,8,11},
      {1,10,13},{2,3,7},{2,4,11},{2,5,13},{2,8,12},{3,10,11},
      {3,12,13},{7,11,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,11},{2,5,13},{2,6,10},{2,8,12},{2,9,7},
 {3,6,7},{3,8,9},{3,10,11},{3,12,13},{4,5,8},{4,9,13},{4,10,12},{5,9,12},
 {5,11,7},{6,8,13},{6,9,11},{8,10,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,10},{6,12},{11,13}}
 Examples of antimorphisms:
   B: \alpha=(0 8)(1 6 9 12)(2 7 13 10)(3 4 11 5)
      B_1={{0,1,2},{0,9,10},{0,13,7},{1,3,5},{1,8,11},{1,12,7},
      {2,4,11},{2,5,13},{2,6,10},{3,8,9},{3,12,13},{4,5,8},
      {4,9,13},{6,9,11}}
   C: \alpha=(0 3 11 7)(1 8 10 5 13 4 2 9)(6 12)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,4,6},
      {1,8,11},{1,10,13},{2,4,11},{2,5,13},{2,6,10},{3,10,11},
      {6,8,13},{6,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,4,11},{2,5,13},{2,6,10},{2,9,8},
 {3,6,8},{3,10,11},{3,12,13},{4,7,8},{4,9,13},{4,10,12},{5,7,10},{5,9,12},
 {5,11,8},{6,7,12},{6,9,11},{7,11,13}}
 I={{0,7},{1,11},{2,12},{3,9},{4,5},{6,13},{10,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,7},{2,4,11},{2,5,13},{2,6,10},{2,8,12},
 {3,6,9},{3,10,11},{3,12,13},{4,5,8},{4,7,9},{4,10,12},{5,7,10},{5,11,9},
 {6,7,12},{6,8,13},{7,11,13},{8,10,9}}
 I={{0,10},{1,7},{2,9},{3,8},{4,13},{5,12},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,7},{2,4,11},{2,5,13},{2,8,12},{2,9,10},
 {3,6,10},{3,8,9},{3,12,13},{4,5,8},{4,7,10},{4,9,13},{5,9,12},{5,11,10},
 {6,7,12},{6,8,13},{6,9,11},{7,11,13}}
 I={{0,9},{1,13},{2,6},{3,11},{4,12},{5,7},{8,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,7},{2,5,13},{2,6,10},{2,8,12},{2,9,11},
 {3,6,11},{3,8,9},{3,12,13},{4,5,8},{4,7,11},{4,9,13},{4,10,12},{5,7,10},
 {5,9,12},{6,7,12},{6,8,13},{8,10,11}}
 I={{0,12},{1,8},{2,4},{3,10},{5,11},{6,9},{7,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,11},{2,5,13},{2,6,10},{2,9,12},
 {3,6,12},{3,8,9},{3,10,11},{4,5,8},{4,7,12},{4,9,13},{5,7,10},{5,11,12},
 {6,8,13},{6,9,11},{7,11,13},{8,10,12}}
 I={{0,11},{1,12},{2,8},{3,13},{4,10},{5,9},{6,7}}
 Examples of antimorphisms:
   B: \alpha=(0 11)(1 12)(2 8)(3 13)(4)(5 9)(6 7)(10)
      B_1={{0,1,2},{0,9,10},{0,13,12},{1,4,6},{1,7,9},{1,10,13},
      {2,3,7},{2,4,11},{2,5,13},{2,6,10},{2,9,12},{4,9,13},
      {6,9,11},{7,11,13}}
 # of antimorphisms of SASC-graph: 1 (fair: 1) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,4,11},{2,6,10},{2,8,12},{2,9,13},
 {3,6,13},{3,8,9},{3,10,11},{4,5,8},{4,7,13},{4,10,12},{5,7,10},{5,9,12},
 {5,11,13},{6,7,12},{6,9,11},{8,10,13}}
 I={{0,13},{1,10},{2,5},{3,12},{4,9},{6,8},{7,11}}
 Examples of antimorphisms:
   A: \alpha=(0 8 3 11)(1 12 7 4)(2 5)(6 9 10 13)
      B_1={{0,3,4},{0,11,12},{1,7,9},{1,12,13},{2,4,11},{2,8,12},
      {2,9,13},{3,8,9},{4,5,8},{4,7,13},{5,9,12},{5,11,13},
      {6,9,11},{8,10,13}}
   C: \alpha=(0 8 3 11)(1 12 7 4)(2)(5)(6 9 10 13)
      B_1={{0,1,2},{0,3,4},{0,9,10},{0,11,12},{1,7,9},{1,12,13},
      {2,3,7},{2,6,10},{3,6,13},{3,8,9},{4,5,8},{4,7,13},
      {5,9,12},{5,11,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,11},{2,5,13},{2,6,10},{2,8,12},
 {3,8,9},{3,10,11},{3,12,13},{4,5,8},{4,9,13},{4,10,12},{5,7,10},{5,9,12},
 {6,7,12},{6,8,13},{6,9,11},{7,11,13}}
 I={{0,13},{1,12},{2,9},{3,6},{4,7},{5,11},{8,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 67 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,9},
 {2,5,12},{2,6,11},{2,8,13},{2,10,0},{3,6,0},{3,8,9},{3,10,11},{3,12,13},
 {4,5,10},{4,7,0},{4,8,12},{4,11,13},{5,7,11},{5,8,0},{5,9,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,9},
 {2,5,12},{2,6,11},{2,8,13},{2,10,1},{3,6,1},{3,8,9},{3,10,11},{3,12,13},
 {4,5,10},{4,7,1},{4,8,12},{4,11,13},{5,7,11},{5,8,1},{5,9,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,11},{3,12,13},
 {4,5,10},{4,7,2},{4,8,12},{4,11,13},{5,7,11},{5,8,2},{5,9,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,2}}
 I={{0,1},{3,7},{4,9},{5,12},{6,11},{8,13},{10,2}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,9},{2,5,12},{2,6,11},{2,8,13},{2,10,3},
 {4,5,10},{4,7,3},{4,8,12},{4,11,13},{5,7,11},{5,8,3},{5,9,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,9},{10,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,12},{2,6,11},{2,8,13},{2,10,4},
 {3,6,4},{3,8,9},{3,10,11},{3,12,13},{5,7,11},{5,8,4},{5,9,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,4}}
 I={{0,3},{1,6},{2,9},{5,10},{7,4},{8,12},{11,13}}
 Examples of antimorphisms:
   B: \alpha=(0 7 6 9)(1 2 3 4)(5 10)(8 13 12 11)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,13,4},{1,3,5},{1,8,11},
      {1,10,13},{2,6,11},{3,6,4},{3,10,11},{3,12,13},{5,7,11},
      {5,9,13},{6,9,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,9},{2,6,11},{2,8,13},{2,10,5},
 {3,6,5},{3,8,9},{3,10,11},{3,12,13},{4,7,5},{4,8,12},{4,11,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,5}}
 I={{0,6},{1,3},{2,12},{4,10},{7,11},{8,5},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,6},{2,3,7},{2,4,9},{2,5,12},{2,8,13},{2,10,6},
 {3,8,9},{3,10,11},{3,12,13},{4,5,10},{4,7,6},{4,8,12},{4,11,13},{5,7,11},
 {5,8,6},{5,9,13},{7,10,12},{9,11,6}}
 I={{0,5},{1,4},{2,11},{3,6},{7,13},{8,10},{9,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,9},{2,5,12},{2,6,11},{2,8,13},{2,10,7},
 {3,6,7},{3,8,9},{3,10,11},{3,12,13},{4,5,10},{4,8,12},{4,11,13},{5,8,7},
 {5,9,13},{6,8,10},{6,9,12},{9,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,11},{6,13},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,4,9},{2,5,12},{2,6,11},{2,10,8},
 {3,6,8},{3,10,11},{3,12,13},{4,5,10},{4,7,8},{4,11,13},{5,7,11},{5,9,13},
 {6,7,13},{6,9,12},{7,10,12},{9,11,8}}
 I={{0,7},{1,11},{2,13},{3,9},{4,12},{5,8},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,7},{2,5,12},{2,6,11},{2,8,13},{2,10,9},
 {3,6,9},{3,10,11},{3,12,13},{4,5,10},{4,7,9},{4,8,12},{4,11,13},{5,7,11},
 {5,8,9},{6,7,13},{6,8,10},{7,10,12}}
 I={{0,10},{1,7},{2,4},{3,8},{5,13},{6,12},{11,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,7},{2,4,9},{2,5,12},{2,6,11},{2,8,13},
 {3,6,10},{3,8,9},{3,12,13},{4,7,10},{4,8,12},{4,11,13},{5,7,11},{5,8,10},
 {5,9,13},{6,7,13},{6,9,12},{9,11,10}}
 I={{0,9},{1,13},{2,10},{3,11},{4,5},{6,8},{7,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,7},{2,4,9},{2,5,12},{2,8,13},{2,10,11},
 {3,6,11},{3,8,9},{3,12,13},{4,5,10},{4,7,11},{4,8,12},{5,8,11},{5,9,13},
 {6,7,13},{6,8,10},{6,9,12},{7,10,12}}
 I={{0,12},{1,8},{2,6},{3,10},{4,13},{5,7},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,9},{2,6,11},{2,8,13},{2,10,12},
 {3,6,12},{3,8,9},{3,10,11},{4,5,10},{4,7,12},{4,11,13},{5,7,11},{5,8,12},
 {5,9,13},{6,7,13},{6,8,10},{9,11,12}}
 I={{0,11},{1,12},{2,5},{3,13},{4,8},{6,9},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,4,9},{2,5,12},{2,6,11},{2,10,13},
 {3,6,13},{3,8,9},{3,10,11},{4,5,10},{4,7,13},{4,8,12},{5,7,11},{5,8,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,13}}
 I={{0,13},{1,10},{2,8},{3,12},{4,11},{5,9},{6,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,9},{2,5,12},{2,6,11},{2,8,13},
 {3,8,9},{3,10,11},{3,12,13},{4,5,10},{4,8,12},{4,11,13},{5,7,11},{5,9,13},
 {6,7,13},{6,8,10},{6,9,12},{7,10,12}}
 I={{0,13},{1,12},{2,10},{3,6},{4,7},{5,8},{9,11}}
 Examples of antimorphisms:
   A: \alpha=(0 1 10 11)(2 6 5 12 9 13 3 8)(4)(7)
      B_1={{0,1,2},{0,3,4},{0,9,10},{1,3,5},{1,7,9},{2,3,7},
      {2,4,9},{2,5,12},{2,6,11},{3,8,9},{3,10,11},{4,5,10},
      {5,7,11},{5,9,13}}
   C: \alpha=(0 6 8 12)(1 2 11 5)(3 10 4 13 9 7)
      B_1={{0,1,2},{0,11,12},{1,4,6},{1,7,9},{1,8,11},{1,10,13},
      {3,10,11},{3,12,13},{4,11,13},{5,7,11},{6,7,13},{6,8,10},
      {6,9,12},{7,10,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 68 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,8},
 {2,5,10},{2,6,13},{2,9,12},{2,11,0},{3,6,0},{3,8,9},{3,10,11},{3,12,13},
 {4,5,11},{4,7,0},{4,9,13},{4,10,12},{5,7,12},{5,8,13},{5,9,0},{6,7,10},
 {6,8,12},{6,9,11},{7,11,13},{8,10,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,8},
 {2,5,10},{2,6,13},{2,9,12},{2,11,1},{3,6,1},{3,8,9},{3,10,11},{3,12,13},
 {4,5,11},{4,7,1},{4,9,13},{4,10,12},{5,7,12},{5,8,13},{5,9,1},{6,7,10},
 {6,8,12},{6,9,11},{7,11,13},{8,10,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,11},{3,12,13},
 {4,5,11},{4,7,2},{4,9,13},{4,10,12},{5,7,12},{5,8,13},{5,9,2},{6,7,10},
 {6,8,12},{6,9,11},{7,11,13},{8,10,2}}
 I={{0,1},{3,7},{4,8},{5,10},{6,13},{9,12},{11,2}}
 Examples of antimorphisms:
   A: \alpha=(0 8 3 12)(1 4 7 9 13 11 6 2)(5 10)
      B_1={{0,3,4},{0,9,10},{0,11,12},{0,13,2},{1,4,6},{1,7,9},
      {1,10,13},{3,6,2},{3,8,9},{3,10,11},{4,10,12},{6,7,10},
      {7,11,13},{8,10,2}}
   C: \alpha=(0 7 12 11 13 9)(1 8 5 2)(3 6 4 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,2},{1,10,13},
      {1,12,2},{3,6,2},{3,12,13},{4,9,13},{4,10,12},{5,8,13},
      {6,8,12},{8,10,2}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,8},{2,5,10},{2,6,13},{2,9,12},{2,11,3},
 {4,5,11},{4,7,3},{4,9,13},{4,10,12},{5,7,12},{5,8,13},{5,9,3},{6,7,10},
 {6,8,12},{6,9,11},{7,11,13},{8,10,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,9},{10,11},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 5 8 1 4 9)(2 7)(3 12 10 6 13 11)
      B_1={{0,1,2},{0,5,6},{0,13,3},{1,8,11},{1,10,13},{2,4,8},
      {2,5,10},{2,6,13},{2,9,12},{2,11,3},{4,9,13},{4,10,12},
      {5,9,3},{8,10,3}}
   B: \alpha=(0 10 5 13)(1 12 4 11)(2 8 7 9)(3 6)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{1,7,9},{1,12,3},
      {2,4,8},{2,6,13},{2,11,3},{4,5,11},{4,7,3},{5,7,12},
      {5,8,13},{6,7,10}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,10},{2,6,13},{2,9,12},{2,11,4},
 {3,6,4},{3,8,9},{3,10,11},{3,12,13},{5,7,12},{5,8,13},{5,9,4},{6,7,10},
 {6,8,12},{6,9,11},{7,11,13},{8,10,4}}
 I={{0,3},{1,6},{2,8},{5,11},{7,4},{9,13},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,11,5},
 {3,6,5},{3,8,9},{3,10,11},{3,12,13},{4,7,5},{4,9,13},{4,10,12},{6,7,10},
 {6,8,12},{6,9,11},{7,11,13},{8,10,5}}
 I={{0,6},{1,3},{2,10},{4,11},{7,12},{8,13},{9,5}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,6},{2,3,7},{2,4,8},{2,5,10},{2,9,12},{2,11,6},
 {3,8,9},{3,10,11},{3,12,13},{4,5,11},{4,7,6},{4,9,13},{4,10,12},{5,7,12},
 {5,8,13},{5,9,6},{7,11,13},{8,10,6}}
 I={{0,5},{1,4},{2,13},{3,6},{7,10},{8,12},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,8},{2,5,10},{2,6,13},{2,9,12},{2,11,7},
 {3,6,7},{3,8,9},{3,10,11},{3,12,13},{4,5,11},{4,9,13},{4,10,12},{5,8,13},
 {5,9,7},{6,8,12},{6,9,11},{8,10,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,12},{6,10},{11,13}}
 Examples of antimorphisms:
   C: \alpha=(0 8)(1 3 4 2 9 7)(5 12)(6)(10)(11 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},
      {1,10,13},{1,12,7},{2,6,13},{2,9,12},{3,6,7},{3,12,13},
      {4,9,13},{4,10,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,5,10},{2,6,13},{2,9,12},{2,11,8},
 {3,6,8},{3,10,11},{3,12,13},{4,5,11},{4,7,8},{4,9,13},{4,10,12},{5,7,12},
 {5,9,8},{6,7,10},{6,9,11},{7,11,13}}
 I={{0,7},{1,11},{2,4},{3,9},{5,13},{6,12},{10,8}}
 Examples of antimorphisms:
   B: \alpha=(0 7)(1)(2 3 4 9)(5 6 13 12)(8 10)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},
      {1,4,6},{1,12,8},{2,9,12},{3,6,8},{3,10,11},{3,12,13},
      {5,9,8},{6,9,11}}
   C: \alpha=(0 9 1 3 12 11 6 4 2 7 5 13)(8 10)
      B_1={{0,3,4},{0,13,8},{1,7,9},{1,12,8},{2,3,7},{2,11,8},
      {3,6,8},{3,12,13},{4,5,11},{4,7,8},{4,9,13},{5,9,8},
      {6,9,11},{7,11,13}}
   D: \alpha=(0 7)(1)(2 9 4 3)(5 12 13 6)(8 10)(11)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},
      {1,4,6},{1,12,8},{2,9,12},{3,6,8},{3,10,11},{3,12,13},
      {5,9,8},{6,9,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,7},{2,4,8},{2,5,10},{2,6,13},{2,11,9},
 {3,6,9},{3,10,11},{3,12,13},{4,5,11},{4,7,9},{4,10,12},{5,7,12},{5,8,13},
 {6,7,10},{6,8,12},{7,11,13},{8,10,9}}
 I={{0,10},{1,7},{2,12},{3,8},{4,13},{5,9},{6,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,7},{2,4,8},{2,6,13},{2,9,12},{2,11,10},
 {3,6,10},{3,8,9},{3,12,13},{4,5,11},{4,7,10},{4,9,13},{5,7,12},{5,8,13},
 {5,9,10},{6,8,12},{6,9,11},{7,11,13}}
 I={{0,9},{1,13},{2,5},{3,11},{4,12},{6,7},{8,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,7},{2,4,8},{2,5,10},{2,6,13},{2,9,12},
 {3,6,11},{3,8,9},{3,12,13},{4,7,11},{4,9,13},{4,10,12},{5,7,12},{5,8,13},
 {5,9,11},{6,7,10},{6,8,12},{8,10,11}}
 I={{0,12},{1,8},{2,11},{3,10},{4,5},{6,9},{7,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,8},{2,5,10},{2,6,13},{2,11,12},
 {3,6,12},{3,8,9},{3,10,11},{4,5,11},{4,7,12},{4,9,13},{5,8,13},{5,9,12},
 {6,7,10},{6,9,11},{7,11,13},{8,10,12}}
 I={{0,11},{1,12},{2,9},{3,13},{4,10},{5,7},{6,8}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,4,8},{2,5,10},{2,9,12},{2,11,13},
 {3,6,13},{3,8,9},{3,10,11},{4,5,11},{4,7,13},{4,10,12},{5,7,12},{5,9,13},
 {6,7,10},{6,8,12},{6,9,11},{8,10,13}}
 I={{0,13},{1,10},{2,6},{3,12},{4,9},{5,8},{7,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,8},{2,5,10},{2,6,13},{2,9,12},
 {3,8,9},{3,10,11},{3,12,13},{4,5,11},{4,9,13},{4,10,12},{5,7,12},{5,8,13},
 {6,7,10},{6,8,12},{6,9,11},{7,11,13}}
 I={{0,13},{1,12},{2,11},{3,6},{4,7},{5,9},{8,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 69 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,9},
 {2,5,11},{2,6,12},{2,10,0},{2,8,13},{3,6,0},{3,8,9},{3,10,11},{3,12,13},
 {4,5,10},{4,7,0},{4,8,12},{4,11,13},{5,7,13},{5,8,0},{5,9,12},{6,7,11},
 {6,8,10},{6,9,13},{7,10,12},{9,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,9},
 {2,5,11},{2,6,12},{2,10,1},{2,8,13},{3,6,1},{3,8,9},{3,10,11},{3,12,13},
 {4,5,10},{4,7,1},{4,8,12},{4,11,13},{5,7,13},{5,8,1},{5,9,12},{6,7,11},
 {6,8,10},{6,9,13},{7,10,12},{9,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 7 3 10 9 11)(1 12 8 2 5 6 4 13)
      B_1={{0,7,8},{2,5,11},{2,10,1},{3,10,11},{4,5,10},{4,7,1},
      {4,8,12},{4,11,13},{5,7,13},{5,8,1},{6,7,11},{6,8,10},
      {7,10,12},{9,11,1}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,11},{3,12,13},
 {4,5,10},{4,7,2},{4,8,12},{4,11,13},{5,7,13},{5,8,2},{5,9,12},{6,7,11},
 {6,8,10},{6,9,13},{7,10,12},{9,11,2}}
 I={{0,1},{3,7},{4,9},{5,11},{6,12},{10,2},{8,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,9},{2,5,11},{2,6,12},{2,10,3},{2,8,13},
 {4,5,10},{4,7,3},{4,8,12},{4,11,13},{5,7,13},{5,8,3},{5,9,12},{6,7,11},
 {6,8,10},{6,9,13},{7,10,12},{9,11,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,9},{10,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,11},{2,6,12},{2,10,4},{2,8,13},
 {3,6,4},{3,8,9},{3,10,11},{3,12,13},{5,7,13},{5,8,4},{5,9,12},{6,7,11},
 {6,8,10},{6,9,13},{7,10,12},{9,11,4}}
 I={{0,3},{1,6},{2,9},{5,10},{7,4},{8,12},{11,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,9},{2,6,12},{2,10,5},{2,8,13},
 {3,6,5},{3,8,9},{3,10,11},{3,12,13},{4,7,5},{4,8,12},{4,11,13},{6,7,11},
 {6,8,10},{6,9,13},{7,10,12},{9,11,5}}
 I={{0,6},{1,3},{2,11},{4,10},{7,13},{8,5},{9,12}}
 Examples of antimorphisms:
   C: \alpha=(0 3 5 2 1 10)(4 6 8 7 12 11 13 9)
      B_1={{0,3,4},{1,10,13},{2,3,7},{2,4,9},{2,6,12},{2,10,5},
      {2,8,13},{3,8,9},{3,10,11},{3,12,13},{4,8,12},{4,11,13},
      {6,8,10},{7,10,12}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,6},{2,3,7},{2,4,9},{2,5,11},{2,10,6},{2,8,13},
 {3,8,9},{3,10,11},{3,12,13},{4,5,10},{4,7,6},{4,8,12},{4,11,13},{5,7,13},
 {5,8,6},{5,9,12},{7,10,12},{9,11,6}}
 I={{0,5},{1,4},{2,12},{3,6},{7,11},{8,10},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,9},{2,5,11},{2,6,12},{2,10,7},{2,8,13},
 {3,6,7},{3,8,9},{3,10,11},{3,12,13},{4,5,10},{4,8,12},{4,11,13},{5,8,7},
 {5,9,12},{6,8,10},{6,9,13},{9,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,13},{6,11},{10,12}}
 Examples of antimorphisms:
   C: \alpha=(0 1 7 8 9 4)(2 3)(5 10 6 13 11 12)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,13,7},{1,3,5},{1,12,7},
      {3,6,7},{3,8,9},{3,10,11},{3,12,13},{4,11,13},{5,9,12},
      {6,8,10},{9,11,7}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,4,9},{2,5,11},{2,6,12},{2,10,8},
 {3,6,8},{3,10,11},{3,12,13},{4,5,10},{4,7,8},{4,11,13},{5,7,13},{5,9,12},
 {6,7,11},{6,9,13},{7,10,12},{9,11,8}}
 I={{0,7},{1,11},{2,13},{3,9},{4,12},{5,8},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,7},{2,5,11},{2,6,12},{2,10,9},{2,8,13},
 {3,6,9},{3,10,11},{3,12,13},{4,5,10},{4,7,9},{4,8,12},{4,11,13},{5,7,13},
 {5,8,9},{6,7,11},{6,8,10},{7,10,12}}
 I={{0,10},{1,7},{2,4},{3,8},{5,12},{6,13},{11,9}}
 Examples of antimorphisms:
   A: \alpha=(0 9 4 12)(1 3 11 2)(5 10 7 8)(6 13)
      B_1={{0,5,6},{0,11,12},{1,3,5},{1,4,6},{1,12,9},{2,3,7},
      {2,5,11},{2,6,12},{3,6,9},{4,7,9},{5,8,9},{6,7,11},
      {6,8,10},{7,10,12}}
   C: \alpha=(0 1 8 10 2 11)(3 4 6 9 7 13)(5 12)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{1,3,5},{2,3,7},
      {2,5,11},{2,8,13},{3,6,9},{4,5,10},{5,7,13},{5,8,9},
      {6,7,11},{6,8,10}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,7},{2,4,9},{2,5,11},{2,6,12},{2,8,13},
 {3,6,10},{3,8,9},{3,12,13},{4,7,10},{4,8,12},{4,11,13},{5,7,13},{5,8,10},
 {5,9,12},{6,7,11},{6,9,13},{9,11,10}}
 I={{0,9},{1,13},{2,10},{3,11},{4,5},{6,8},{7,12}}
 Examples of antimorphisms:
   A: \alpha=(0 2 7 5)(1 3 4 9)(6 8)(10 12 13 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,13,10},{1,4,6},{1,7,9},
      {1,8,11},{1,12,10},{2,8,13},{4,7,10},{4,8,12},{4,11,13},
      {5,7,13},{5,8,10}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,7},{2,4,9},{2,6,12},{2,10,11},{2,8,13},
 {3,6,11},{3,8,9},{3,12,13},{4,5,10},{4,7,11},{4,8,12},{5,7,13},{5,8,11},
 {5,9,12},{6,8,10},{6,9,13},{7,10,12}}
 I={{0,12},{1,8},{2,5},{3,10},{4,13},{6,7},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,9},{2,5,11},{2,10,12},{2,8,13},
 {3,6,12},{3,8,9},{3,10,11},{4,5,10},{4,7,12},{4,11,13},{5,7,13},{5,8,12},
 {6,7,11},{6,8,10},{6,9,13},{9,11,12}}
 I={{0,11},{1,12},{2,6},{3,13},{4,8},{5,9},{7,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,4,9},{2,5,11},{2,6,12},{2,10,13},
 {3,6,13},{3,8,9},{3,10,11},{4,5,10},{4,7,13},{4,8,12},{5,8,13},{5,9,12},
 {6,7,11},{6,8,10},{7,10,12},{9,11,13}}
 I={{0,13},{1,10},{2,8},{3,12},{4,11},{5,7},{6,9}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,9},{2,5,11},{2,6,12},{2,8,13},
 {3,8,9},{3,10,11},{3,12,13},{4,5,10},{4,8,12},{4,11,13},{5,7,13},{5,9,12},
 {6,7,11},{6,8,10},{6,9,13},{7,10,12}}
 I={{0,13},{1,12},{2,10},{3,6},{4,7},{5,8},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 70 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,13},
 {2,5,11},{2,6,10},{2,8,0},{2,9,12},{3,6,0},{3,8,9},{3,10,12},{3,11,13},
 {4,5,12},{4,7,0},{4,8,10},{4,9,11},{5,7,10},{5,8,13},{5,9,0},{6,7,11},
 {6,8,12},{6,9,13},{7,12,13},{10,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,13},
 {2,5,11},{2,6,10},{2,8,1},{2,9,12},{3,6,1},{3,8,9},{3,10,12},{3,11,13},
 {4,5,12},{4,7,1},{4,8,10},{4,9,11},{5,7,10},{5,8,13},{5,9,1},{6,7,11},
 {6,8,12},{6,9,13},{7,12,13},{10,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,12},{3,11,13},
 {4,5,12},{4,7,2},{4,8,10},{4,9,11},{5,7,10},{5,8,13},{5,9,2},{6,7,11},
 {6,8,12},{6,9,13},{7,12,13},{10,11,2}}
 I={{0,1},{3,7},{4,13},{5,11},{6,10},{8,2},{9,12}}
 Examples of antimorphisms:
   A: \alpha=(0 6 3 11)(1 13 12 5)(2 8)(4 9 10 7)
      B_1={{0,5,6},{0,7,8},{1,8,11},{1,10,13},{3,8,9},{3,11,13},
      {4,5,12},{4,8,10},{4,9,11},{5,7,10},{5,8,13},{6,7,11},
      {6,8,12},{6,9,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,13},{2,5,11},{2,6,10},{2,8,3},{2,9,12},
 {4,5,12},{4,7,3},{4,8,10},{4,9,11},{5,7,10},{5,8,13},{5,9,3},{6,7,11},
 {6,8,12},{6,9,13},{7,12,13},{10,11,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,9},{10,12},{11,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,11},{2,6,10},{2,8,4},{2,9,12},
 {3,6,4},{3,8,9},{3,10,12},{3,11,13},{5,7,10},{5,8,13},{5,9,4},{6,7,11},
 {6,8,12},{6,9,13},{7,12,13},{10,11,4}}
 I={{0,3},{1,6},{2,13},{5,12},{7,4},{8,10},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,13},{2,6,10},{2,8,5},{2,9,12},
 {3,6,5},{3,8,9},{3,10,12},{3,11,13},{4,7,5},{4,8,10},{4,9,11},{6,7,11},
 {6,8,12},{6,9,13},{7,12,13},{10,11,5}}
 I={{0,6},{1,3},{2,11},{4,12},{7,10},{8,13},{9,5}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,6},{2,3,7},{2,4,13},{2,5,11},{2,8,6},{2,9,12},
 {3,8,9},{3,10,12},{3,11,13},{4,5,12},{4,7,6},{4,8,10},{4,9,11},{5,7,10},
 {5,8,13},{5,9,6},{7,12,13},{10,11,6}}
 I={{0,5},{1,4},{2,10},{3,6},{7,11},{8,12},{9,13}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 13 4 9)(2 10)(3 6)(5)(7 11)(8 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{1,3,5},{1,7,9},{1,12,6},
      {2,3,7},{2,4,13},{2,5,11},{2,8,6},{2,9,12},{4,5,12},
      {4,7,6},{7,12,13}}
   C: \alpha=(0 10 3 13)(1 4)(2 8 7 5)(6 9 12 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{1,3,5},
      {1,7,9},{1,8,11},{1,12,6},{2,3,7},{2,5,11},{3,8,9},
      {3,11,13},{5,9,6}}
   D: \alpha=(0)(1 9 4 13)(2 10)(3 6)(5)(7 11)(8 12)
      B_1={{0,1,2},{0,3,4},{0,7,8},{1,3,5},{1,7,9},{1,12,6},
      {2,3,7},{2,4,13},{2,5,11},{2,8,6},{2,9,12},{4,5,12},
      {4,7,6},{7,12,13}}
 # of antimorphisms of SASC-graph: 8 (fair: 6) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,13},{2,5,11},{2,6,10},{2,8,7},{2,9,12},
 {3,6,7},{3,8,9},{3,10,12},{3,11,13},{4,5,12},{4,8,10},{4,9,11},{5,8,13},
 {5,9,7},{6,8,12},{6,9,13},{10,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,10},{6,11},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,4,13},{2,5,11},{2,6,10},{2,9,12},
 {3,6,8},{3,10,12},{3,11,13},{4,5,12},{4,7,8},{4,9,11},{5,7,10},{5,9,8},
 {6,7,11},{6,9,13},{7,12,13},{10,11,8}}
 I={{0,7},{1,11},{2,8},{3,9},{4,10},{5,13},{6,12}}
 Examples of antimorphisms:
   C: \alpha=(0 5 11 9)(1 6 2 13)(3 7 12 8)(4 10)
      B_1={{0,3,4},{0,5,6},{0,11,12},{1,3,5},{1,10,13},{2,6,10},
      {2,9,12},{3,6,8},{3,11,13},{4,5,12},{4,7,8},{4,9,11},
      {6,9,13},{7,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,7},{2,4,13},{2,5,11},{2,6,10},{2,8,9},
 {3,6,9},{3,10,12},{3,11,13},{4,5,12},{4,7,9},{4,8,10},{5,7,10},{5,8,13},
 {6,7,11},{6,8,12},{7,12,13},{10,11,9}}
 I={{0,10},{1,7},{2,12},{3,8},{4,11},{5,9},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 9 7)(1 12 13 10 5 6)(3 8)(4 11)
      B_1={{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,8,11},
      {1,10,13},{1,12,9},{2,5,11},{2,8,9},{3,11,13},{5,8,13},
      {6,7,11},{10,11,9}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,7},{2,4,13},{2,5,11},{2,8,10},{2,9,12},
 {3,6,10},{3,8,9},{3,11,13},{4,5,12},{4,7,10},{4,9,11},{5,8,13},{5,9,10},
 {6,7,11},{6,8,12},{6,9,13},{7,12,13}}
 I={{0,9},{1,13},{2,6},{3,12},{4,8},{5,7},{11,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,7},{2,4,13},{2,6,10},{2,8,11},{2,9,12},
 {3,6,11},{3,8,9},{3,10,12},{4,5,12},{4,7,11},{4,8,10},{5,7,10},{5,8,13},
 {5,9,11},{6,8,12},{6,9,13},{7,12,13}}
 I={{0,12},{1,8},{2,5},{3,13},{4,9},{6,7},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,13},{2,5,11},{2,6,10},{2,8,12},
 {3,6,12},{3,8,9},{3,11,13},{4,7,12},{4,8,10},{4,9,11},{5,7,10},{5,8,13},
 {5,9,12},{6,7,11},{6,9,13},{10,11,12}}
 I={{0,11},{1,12},{2,9},{3,10},{4,5},{6,8},{7,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 9 3 4 13 6 8)(1 11 5 12 10 7)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,4,6},{1,7,9},
      {2,4,13},{2,5,11},{3,6,12},{3,8,9},{4,7,12},{4,9,11},
      {6,7,11},{10,11,12}}
   C: \alpha=(0 4 8 9)(1 12)(2 7 11 5 13 6)(3 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,13,12},{1,8,11},
      {1,10,13},{2,6,10},{2,8,12},{3,8,9},{5,7,10},{5,8,13},
      {6,7,11},{10,11,12}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,5,11},{2,6,10},{2,8,13},{2,9,12},
 {3,6,13},{3,8,9},{3,10,12},{4,5,12},{4,7,13},{4,8,10},{4,9,11},{5,7,10},
 {5,9,13},{6,7,11},{6,8,12},{10,11,13}}
 I={{0,13},{1,10},{2,4},{3,11},{5,8},{6,9},{7,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,13},{2,5,11},{2,6,10},{2,9,12},
 {3,8,9},{3,10,12},{3,11,13},{4,5,12},{4,8,10},{4,9,11},{5,7,10},{5,8,13},
 {6,7,11},{6,8,12},{6,9,13},{7,12,13}}
 I={{0,13},{1,12},{2,8},{3,6},{4,7},{5,9},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 5 10 13 2 12)(1 11 3 7)(4 9 8 6)
      B_1={{0,7,8},{0,11,12},{1,7,9},{2,4,13},{2,5,11},{3,11,13},
      {4,5,12},{4,8,10},{4,9,11},{5,7,10},{5,8,13},{6,7,11},
      {6,8,12},{7,12,13}}
   B: \alpha=(0 13)(1 8 10 7)(2 11 4 12)(3)(5 9)(6)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},
      {1,4,6},{1,7,9},{2,3,7},{2,5,11},{2,6,10},{3,8,9},
      {4,5,12},{4,8,10}}
   C: \alpha=(0 4 9 8 6 5 10 13 2 12)(1 11 3 7)
      B_1={{0,7,8},{0,11,12},{1,7,9},{2,4,13},{2,5,11},{3,11,13},
      {4,5,12},{4,8,10},{4,9,11},{5,7,10},{5,8,13},{6,7,11},
      {6,8,12},{7,12,13}}
   D: \alpha=(0 13)(1 7 10 8)(2 12 4 11)(3)(5 9)(6)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},
      {1,4,6},{1,7,9},{2,3,7},{2,5,11},{2,6,10},{3,8,9},
      {4,5,12},{4,8,10}}
 # of antimorphisms of SASC-graph: 15 (fair: 3) 
 # of halving permutations: 5 (fair: 1; strong: 0) 


 System No. 71 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,12},
 {2,5,10},{2,6,11},{2,8,13},{2,9,0},{3,6,0},{3,8,9},{3,10,12},{3,11,13},
 {4,5,13},{4,7,0},{4,8,10},{4,9,11},{5,7,11},{5,8,0},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 6 10 11 1 12 2 5 9 7 13 8)(3 4)
      B_1={{1,4,6},{1,8,11},{2,4,12},{2,6,11},{4,5,13},{4,7,0},
      {4,8,10},{4,9,11},{5,7,11},{5,8,0},{5,9,12},{6,7,10},
      {6,8,12},{7,12,13}}
   B: \alpha=(0 7 2 11)(1 12 13 8)(3 4)(5 9 6 10)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{2,3,7},
      {2,5,10},{2,9,0},{3,6,0},{3,11,13},{4,5,13},{6,9,13},
      {7,12,13},{10,11,0}}
   C: \alpha=(0 2 11 7)(1 12 4 9)(3 10 8 13)(5 6)
      B_1={{1,8,11},{1,12,0},{2,3,7},{2,6,11},{2,8,13},{3,6,0},
      {3,8,9},{3,10,12},{4,7,0},{4,9,11},{5,9,12},{6,7,10},
      {6,8,12},{6,9,13}}
   D: \alpha=(0 11 2 7)(1 8 13 12)(3 4)(5 10 6 9)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{2,3,7},
      {2,5,10},{2,9,0},{3,6,0},{3,11,13},{4,5,13},{6,9,13},
      {7,12,13},{10,11,0}}
 # of antimorphisms of SASC-graph: 8 (fair: 2) 
 # of halving permutations: 5 (fair: 1; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,12},
 {2,5,10},{2,6,11},{2,8,13},{2,9,1},{3,6,1},{3,8,9},{3,10,12},{3,11,13},
 {4,5,13},{4,7,1},{4,8,10},{4,9,11},{5,7,11},{5,8,1},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 3 11 6)(1 12 4 13 10 8 2 5)(7)(9)
      B_1={{0,3,4},{0,9,10},{0,13,1},{2,3,7},{2,4,12},{2,5,10},
      {2,6,11},{2,9,1},{3,6,1},{4,7,1},{4,8,10},{4,9,11},
      {6,7,10},{10,11,1}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,12},{3,11,13},
 {4,5,13},{4,7,2},{4,8,10},{4,9,11},{5,7,11},{5,8,2},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,2}}
 I={{0,1},{3,7},{4,12},{5,10},{6,11},{8,13},{9,2}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,12},{2,5,10},{2,6,11},{2,8,13},{2,9,3},
 {4,5,13},{4,7,3},{4,8,10},{4,9,11},{5,7,11},{5,8,3},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,9},{10,12},{11,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,10},{2,6,11},{2,8,13},{2,9,4},
 {3,6,4},{3,8,9},{3,10,12},{3,11,13},{5,7,11},{5,8,4},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,4}}
 I={{0,3},{1,6},{2,12},{5,13},{7,4},{8,10},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,12},{2,6,11},{2,8,13},{2,9,5},
 {3,6,5},{3,8,9},{3,10,12},{3,11,13},{4,7,5},{4,8,10},{4,9,11},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,5}}
 I={{0,6},{1,3},{2,10},{4,13},{7,11},{8,5},{9,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,6},{2,3,7},{2,4,12},{2,5,10},{2,8,13},{2,9,6},
 {3,8,9},{3,10,12},{3,11,13},{4,5,13},{4,7,6},{4,8,10},{4,9,11},{5,7,11},
 {5,8,6},{5,9,12},{7,12,13},{10,11,6}}
 I={{0,5},{1,4},{2,11},{3,6},{7,10},{8,12},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,12},{2,5,10},{2,6,11},{2,8,13},{2,9,7},
 {3,6,7},{3,8,9},{3,10,12},{3,11,13},{4,5,13},{4,8,10},{4,9,11},{5,8,7},
 {5,9,12},{6,8,12},{6,9,13},{10,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,11},{6,10},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 1 12 3)(2 7 10 13)(4 6 8 9)(5 11)
      B_1={{0,3,4},{0,9,10},{0,13,7},{1,3,5},{1,8,11},{1,12,7},
      {2,4,12},{2,6,11},{2,8,13},{3,11,13},{4,8,10},{4,9,11},
      {6,8,12},{10,11,7}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,4,12},{2,5,10},{2,6,11},{2,9,8},
 {3,6,8},{3,10,12},{3,11,13},{4,5,13},{4,7,8},{4,9,11},{5,7,11},{5,9,12},
 {6,7,10},{6,9,13},{7,12,13},{10,11,8}}
 I={{0,7},{1,11},{2,13},{3,9},{4,10},{5,8},{6,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,7},{2,4,12},{2,5,10},{2,6,11},{2,8,13},
 {3,6,9},{3,10,12},{3,11,13},{4,5,13},{4,7,9},{4,8,10},{5,7,11},{5,8,9},
 {6,7,10},{6,8,12},{7,12,13},{10,11,9}}
 I={{0,10},{1,7},{2,9},{3,8},{4,11},{5,12},{6,13}}
 Examples of antimorphisms:
   A: \alpha=(0 6 2 12)(1 5 10 8)(3 7 13 9)(4 11)
      B_1={{0,3,4},{0,5,6},{1,3,5},{1,4,6},{1,10,13},{2,4,12},
      {2,8,13},{3,6,9},{3,10,12},{4,5,13},{4,7,9},{4,8,10},
      {6,8,12},{7,12,13}}
   C: \alpha=(0 11 8 13)(1 2 6 5 7 3 9 12 4 10)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,13,9},{1,4,6},
      {1,8,11},{1,12,9},{2,3,7},{4,7,9},{4,8,10},{5,8,9},
      {6,7,10},{6,8,12}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,7},{2,4,12},{2,6,11},{2,8,13},{2,9,10},
 {3,6,10},{3,8,9},{3,11,13},{4,5,13},{4,7,10},{4,9,11},{5,7,11},{5,8,10},
 {5,9,12},{6,8,12},{6,9,13},{7,12,13}}
 I={{0,9},{1,13},{2,5},{3,12},{4,8},{6,7},{11,10}}
 Examples of antimorphisms:
   A: \alpha=(0 3 12 9 1 13)(2 5)(4 8 10)(6 7)(11)
      B_1={{0,5,6},{0,13,10},{1,3,5},{1,4,6},{3,6,10},{3,8,9},
      {3,11,13},{4,5,13},{4,9,11},{5,7,11},{5,8,10},{5,9,12},
      {6,8,12},{6,9,13}}
   B: \alpha=(0 9)(1 13)(2 5)(3 12)(4 8)(6 7)(10)(11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,11,12},{1,7,9},{1,8,11},
      {1,12,10},{2,3,7},{2,4,12},{2,6,11},{2,8,13},{2,9,10},
      {4,7,10},{7,12,13}}
   C: \alpha=(0 7 3 13)(1 9 8 2)(4 5 6 12)(10 11)
      B_1={{0,7,8},{0,11,12},{1,3,5},{1,4,6},{1,7,9},{2,6,11},
      {2,8,13},{2,9,10},{3,11,13},{4,5,13},{4,9,11},{5,7,11},
      {6,8,12},{7,12,13}}
 # of antimorphisms of SASC-graph: 9 (fair: 1) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,7},{2,4,12},{2,5,10},{2,8,13},{2,9,11},
 {3,6,11},{3,8,9},{3,10,12},{4,5,13},{4,7,11},{4,8,10},{5,8,11},{5,9,12},
 {6,7,10},{6,8,12},{6,9,13},{7,12,13}}
 I={{0,12},{1,8},{2,6},{3,13},{4,9},{5,7},{10,11}}
 Examples of antimorphisms:
   C: \alpha=(0 1 9 3)(2 7 8 10 5 4)(6 11 13 12)
      B_1={{0,3,4},{0,9,10},{1,4,6},{1,7,9},{1,10,13},{1,12,11},
      {2,3,7},{3,6,11},{3,10,12},{4,5,13},{4,7,11},{4,8,10},
      {6,7,10},{7,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,5,10},{2,6,11},{2,8,13},{2,9,12},
 {3,6,12},{3,8,9},{3,11,13},{4,5,13},{4,7,12},{4,8,10},{4,9,11},{5,7,11},
 {5,8,12},{6,7,10},{6,9,13},{10,11,12}}
 I={{0,11},{1,12},{2,4},{3,10},{5,9},{6,8},{7,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,4,12},{2,5,10},{2,6,11},{2,9,13},
 {3,6,13},{3,8,9},{3,10,12},{4,7,13},{4,8,10},{4,9,11},{5,7,11},{5,8,13},
 {5,9,12},{6,7,10},{6,8,12},{10,11,13}}
 I={{0,13},{1,10},{2,8},{3,11},{4,5},{6,9},{7,12}}
 Examples of antimorphisms:
   A: \alpha=(0 13)(1 3 7 10 11 12)(2 6 8 4 9 5)
      B_1={{1,4,6},{1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,6,11},
      {2,9,13},{3,6,13},{4,7,13},{4,8,10},{5,7,11},{5,8,13},
      {5,9,12},{10,11,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,12},{2,5,10},{2,6,11},{2,8,13},
 {3,8,9},{3,10,12},{3,11,13},{4,5,13},{4,8,10},{4,9,11},{5,7,11},{5,9,12},
 {6,7,10},{6,8,12},{6,9,13},{7,12,13}}
 I={{0,13},{1,12},{2,9},{3,6},{4,7},{5,8},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 7 3 10)(1 13 2 12 11 5 6 9 8 4)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{1,3,5},
      {1,4,6},{1,8,11},{2,3,7},{2,6,11},{2,8,13},{3,8,9},
      {3,11,13},{6,8,12}}
   C: \alpha=(0 2 5 1 8 12 11 6)(3 13 9 10)(4 7)
      B_1={{0,5,6},{0,11,12},{1,4,6},{1,7,9},{1,8,11},{1,10,13},
      {2,3,7},{2,4,12},{2,5,10},{2,8,13},{3,10,12},{6,7,10},
      {6,9,13},{7,12,13}}
 # of antimorphisms of SASC-graph: 6 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 System No. 72 
 |Aut(S)|=1 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,13},
 {2,5,12},{2,6,11},{2,8,10},{2,9,0},{3,6,0},{3,8,9},{3,10,12},{3,11,13},
 {4,5,10},{4,7,0},{4,8,12},{4,9,11},{5,7,11},{5,8,0},{5,9,13},{6,7,10},
 {6,8,13},{6,9,12},{7,12,13},{10,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,13},
 {2,5,12},{2,6,11},{2,8,10},{2,9,1},{3,6,1},{3,8,9},{3,10,12},{3,11,13},
 {4,5,10},{4,7,1},{4,8,12},{4,9,11},{5,7,11},{5,8,1},{5,9,13},{6,7,10},
 {6,8,13},{6,9,12},{7,12,13},{10,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,12},{3,11,13},
 {4,5,10},{4,7,2},{4,8,12},{4,9,11},{5,7,11},{5,8,2},{5,9,13},{6,7,10},
 {6,8,13},{6,9,12},{7,12,13},{10,11,2}}
 I={{0,1},{3,7},{4,13},{5,12},{6,11},{8,10},{9,2}}
 Examples of antimorphisms:
   A: \alpha=(0 5 4 7)(1 6 10 3)(2 8 12 9 11 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,2},{1,4,6},
      {1,8,11},{1,10,13},{1,12,2},{3,10,12},{4,7,2},{4,8,12},
      {4,9,11},{10,11,2}}
   C: \alpha=(0 5 4 7)(1 6 10 3 11 9)(2 8 12 13)
      B_1={{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,2},{1,4,6},
      {1,8,11},{1,10,13},{1,12,2},{3,10,12},{4,7,2},{4,8,12},
      {4,9,11},{10,11,2}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,13},{2,5,12},{2,6,11},{2,8,10},{2,9,3},
 {4,5,10},{4,7,3},{4,8,12},{4,9,11},{5,7,11},{5,8,3},{5,9,13},{6,7,10},
 {6,8,13},{6,9,12},{7,12,13},{10,11,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,9},{10,12},{11,13}}
 Examples of antimorphisms:
   A: \alpha=(0 5 2 6 12 7)(1 11 9 10)(3 13 8 4)
      B_1={{0,5,6},{1,4,6},{1,7,9},{1,10,13},{2,6,11},{4,5,10},
      {4,7,3},{4,9,11},{5,7,11},{5,8,3},{5,9,13},{6,7,10},
      {6,8,13},{7,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,12},{2,6,11},{2,8,10},{2,9,4},
 {3,6,4},{3,8,9},{3,10,12},{3,11,13},{5,7,11},{5,8,4},{5,9,13},{6,7,10},
 {6,8,13},{6,9,12},{7,12,13},{10,11,4}}
 I={{0,3},{1,6},{2,13},{5,10},{7,4},{8,12},{9,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,13},{2,6,11},{2,8,10},{2,9,5},
 {3,6,5},{3,8,9},{3,10,12},{3,11,13},{4,7,5},{4,8,12},{4,9,11},{6,7,10},
 {6,8,13},{6,9,12},{7,12,13},{10,11,5}}
 I={{0,6},{1,3},{2,12},{4,10},{7,11},{8,5},{9,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 6 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,6},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,6},{2,3,7},{2,4,13},{2,5,12},{2,8,10},{2,9,6},
 {3,8,9},{3,10,12},{3,11,13},{4,5,10},{4,7,6},{4,8,12},{4,9,11},{5,7,11},
 {5,8,6},{5,9,13},{7,12,13},{10,11,6}}
 I={{0,5},{1,4},{2,11},{3,6},{7,10},{8,13},{9,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,13},{2,5,12},{2,6,11},{2,8,10},{2,9,7},
 {3,6,7},{3,8,9},{3,10,12},{3,11,13},{4,5,10},{4,8,12},{4,9,11},{5,8,7},
 {5,9,13},{6,8,13},{6,9,12},{10,11,7}}
 I={{0,8},{1,9},{2,3},{4,7},{5,11},{6,10},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 5 8 11 3)(1 13 7 9 12 4)(6 10)
      B_1={{0,3,4},{0,5,6},{0,13,7},{1,4,6},{1,8,11},{2,4,13},
      {2,5,12},{2,6,11},{3,6,7},{3,8,9},{4,9,11},{5,9,13},
      {6,8,13},{6,9,12}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,4,13},{2,5,12},{2,6,11},{2,9,8},
 {3,6,8},{3,10,12},{3,11,13},{4,5,10},{4,7,8},{4,9,11},{5,7,11},{5,9,13},
 {6,7,10},{6,9,12},{7,12,13},{10,11,8}}
 I={{0,7},{1,11},{2,10},{3,9},{4,12},{5,8},{6,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 9 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,9},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,9},{2,3,7},{2,4,13},{2,5,12},{2,6,11},{2,8,10},
 {3,6,9},{3,10,12},{3,11,13},{4,5,10},{4,7,9},{4,8,12},{5,7,11},{5,8,9},
 {6,7,10},{6,8,13},{7,12,13},{10,11,9}}
 I={{0,10},{1,7},{2,9},{3,8},{4,11},{5,13},{6,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 10 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,11,12},{0,13,10},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,10},{2,3,7},{2,4,13},{2,5,12},{2,6,11},{2,9,10},
 {3,6,10},{3,8,9},{3,11,13},{4,7,10},{4,8,12},{4,9,11},{5,7,11},{5,8,10},
 {5,9,13},{6,8,13},{6,9,12},{7,12,13}}
 I={{0,9},{1,13},{2,8},{3,12},{4,5},{6,7},{11,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 11 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,11},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,11},{2,3,7},{2,4,13},{2,5,12},{2,8,10},{2,9,11},
 {3,6,11},{3,8,9},{3,10,12},{4,5,10},{4,7,11},{4,8,12},{5,8,11},{5,9,13},
 {6,7,10},{6,8,13},{6,9,12},{7,12,13}}
 I={{0,12},{1,8},{2,6},{3,13},{4,9},{5,7},{10,11}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 12 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,13},{2,6,11},{2,8,10},{2,9,12},
 {3,6,12},{3,8,9},{3,11,13},{4,5,10},{4,7,12},{4,9,11},{5,7,11},{5,8,12},
 {5,9,13},{6,7,10},{6,8,13},{10,11,12}}
 I={{0,11},{1,12},{2,5},{3,10},{4,8},{6,9},{7,13}}
 Examples of antimorphisms:
   A: \alpha=(0 2 12 4 10 7 11 13)(1 8 6 5 3 9)
      B_1={{0,1,2},{0,3,4},{1,3,5},{1,4,6},{1,7,9},{1,10,13},
      {2,3,7},{2,4,13},{2,6,11},{3,6,12},{3,11,13},{4,7,12},
      {6,7,10},{6,8,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,5,12},{2,6,11},{2,8,10},{2,9,13},
 {3,6,13},{3,8,9},{3,10,12},{4,5,10},{4,7,13},{4,8,12},{4,9,11},{5,7,11},
 {5,8,13},{6,7,10},{6,9,12},{10,11,13}}
 I={{0,13},{1,10},{2,4},{3,11},{5,9},{6,8},{7,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 14 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,13},{2,5,12},{2,6,11},{2,8,10},
 {3,8,9},{3,10,12},{3,11,13},{4,5,10},{4,8,12},{4,9,11},{5,7,11},{5,9,13},
 {6,7,10},{6,8,13},{6,9,12},{7,12,13}}
 I={{0,13},{1,12},{2,9},{3,6},{4,7},{5,8},{10,11}}
 Examples of antimorphisms:
   C: \alpha=(0 13)(1 3 7 5 2 11 8 9)(4 12 6 10)
      B_1={{1,4,6},{1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,13},
      {2,5,12},{2,8,10},{3,11,13},{4,8,12},{5,9,13},{6,7,10},
      {6,8,13},{7,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 73 
 |Aut(S)|=4 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,12},
 {2,5,9},{2,6,11},{2,8,13},{2,10,0},{3,6,0},{3,8,12},{3,9,13},{3,10,11},
 {4,5,10},{4,7,0},{4,8,9},{4,11,13},{5,7,11},{5,8,0},{5,12,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   C: \alpha=(0 1 9 11 8 4 12 7)(2 10 13 3)(5)(6)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{2,3,7},
      {2,4,12},{2,6,11},{3,10,11},{4,5,10},{4,7,0},{4,11,13},
      {5,7,11},{6,7,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,12},
 {2,5,9},{2,6,11},{2,8,13},{2,10,1},{3,6,1},{3,8,12},{3,9,13},{3,10,11},
 {4,5,10},{4,7,1},{4,8,9},{4,11,13},{5,7,11},{5,8,1},{5,12,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=4 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,9},{2,6,11},{2,8,13},{2,10,4},
 {3,6,4},{3,8,12},{3,9,13},{3,10,11},{5,7,11},{5,8,4},{5,12,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,4}}
 I={{0,3},{1,6},{2,12},{5,10},{7,4},{8,9},{11,13}}
 Examples of antimorphisms:
   B: \alpha=(0 2 6 4)(1 7 3 12)(5 10)(8 11 9 13)
      B_1={{0,1,2},{0,5,6},{0,7,8},{1,3,5},{1,7,9},{2,5,9},
      {2,8,13},{3,6,4},{3,8,12},{5,7,11},{5,8,4},{5,12,13},
      {6,9,12},{9,11,4}}
   C: \alpha=(0 2 3 12 9 11 6 4 1 7 8 13)(5 10)
      B_1={{0,5,6},{0,7,8},{0,13,4},{1,3,5},{1,8,11},{1,12,4},
      {2,3,7},{2,5,9},{2,6,11},{3,9,13},{5,7,11},{5,8,4},
      {5,12,13},{6,9,12}}
   E: \alpha=(0 7 6 12)(1 2 3 4)(5 10)(8 13 9 11)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,13,4},{1,3,5},
      {1,8,11},{1,10,13},{2,6,11},{3,6,4},{3,9,13},{3,10,11},
      {6,8,10},{6,9,12}}
 # of antimorphisms of SASC-graph: 20 (fair: 8) 
 # of halving permutations: 14 (fair: 2; strong: 2) 


 Subsystem No. 5 
 |Aut(T)|=2 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,12},{2,6,11},{2,8,13},{2,10,5},
 {3,6,5},{3,8,12},{3,9,13},{3,10,11},{4,7,5},{4,8,9},{4,11,13},{6,7,13},
 {6,8,10},{6,9,12},{7,10,12},{9,11,5}}
 I={{0,6},{1,3},{2,9},{4,10},{7,11},{8,5},{12,13}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,4,12},{2,5,9},{2,6,11},{2,10,8},
 {3,6,8},{3,9,13},{3,10,11},{4,5,10},{4,7,8},{4,11,13},{5,7,11},{5,12,13},
 {6,7,13},{6,9,12},{7,10,12},{9,11,8}}
 I={{0,7},{1,11},{2,13},{3,12},{4,9},{5,8},{6,10}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 System No. 74 
 |Aut(S)|=4 


 Subsystem No. 0 
 |Aut(T)|=4 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,11},{2,6,13},{2,9,0},{2,8,12},{3,6,0},{3,8,13},{3,9,11},{3,10,12},
 {4,5,12},{4,7,0},{4,8,9},{4,11,13},{5,7,10},{5,8,0},{5,9,13},{6,7,11},
 {6,8,10},{6,9,12},{7,12,13},{10,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 3 10 8)(2 4 9 7)(5 11 6 12)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,10,13},{2,4,10},{2,9,0},
      {3,6,0},{4,5,12},{4,11,13},{5,7,10},{5,8,0},{6,7,11},
      {6,8,10},{7,12,13}}
   C: \alpha=(0)(1 3 10 8)(2 7 5 12 9 4 6 11)(13)
      B_1={{1,3,5},{1,10,13},{2,3,7},{2,9,0},{2,8,12},{3,6,0},
      {3,9,11},{4,5,12},{4,8,9},{4,11,13},{5,8,0},{6,7,11},
      {6,8,10},{7,12,13}}
   E: \alpha=(0)(1 3 10 8)(2 4 9 7)(5 12 6 11)(13)
      B_1={{1,3,5},{1,4,6},{1,7,9},{1,10,13},{1,12,0},{2,4,10},
      {2,5,11},{2,6,13},{2,9,0},{5,7,10},{5,9,13},{6,8,10},
      {6,9,12},{10,11,0}}
 # of antimorphisms of SASC-graph: 10 (fair: 6) 
 # of halving permutations: 6 (fair: 2; strong: 2) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,11},{2,6,13},{2,9,1},{2,8,12},{3,6,1},{3,8,13},{3,9,11},{3,10,12},
 {4,5,12},{4,7,1},{4,8,9},{4,11,13},{5,7,10},{5,8,1},{5,9,13},{6,7,11},
 {6,8,10},{6,9,12},{7,12,13},{10,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   B: \alpha=(0 2)(1 10 3 8)(4)(5 11 12 13)(6)(7 9)
      B_1={{0,3,4},{0,5,6},{0,11,12},{0,13,1},{2,3,7},{2,9,1},
      {3,6,1},{3,8,13},{3,9,11},{4,5,12},{4,7,1},{5,9,13},
      {6,9,12},{10,11,1}}
   D: \alpha=(0 2)(1 8 3 10)(4)(5 13 12 11)(6)(7 9)
      B_1={{0,3,4},{0,5,6},{0,11,12},{0,13,1},{2,3,7},{2,9,1},
      {3,6,1},{3,8,13},{3,9,11},{4,5,12},{4,7,1},{5,9,13},
      {6,9,12},{10,11,1}}
 # of antimorphisms of SASC-graph: 4 (fair: 4) 
 # of halving permutations: 2 (fair: 2; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,13},{3,9,11},{3,10,12},
 {4,5,12},{4,7,2},{4,8,9},{4,11,13},{5,7,10},{5,8,2},{5,9,13},{6,7,11},
 {6,8,10},{6,9,12},{7,12,13},{10,11,2}}
 I={{0,1},{3,7},{4,10},{5,11},{6,13},{9,2},{8,12}}
 Examples of antimorphisms:
   A: \alpha=(0 6 12 10)(1 5 7 4)(2 13 3 9 8 11)
      B_1={{0,3,4},{0,5,6},{0,7,8},{1,3,5},{1,12,2},{3,6,2},
      {3,8,13},{3,10,12},{4,5,12},{4,7,2},{4,8,9},{5,8,2},
      {6,8,10},{10,11,2}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,10},{2,6,13},{2,9,5},{2,8,12},
 {3,6,5},{3,8,13},{3,9,11},{3,10,12},{4,7,5},{4,8,9},{4,11,13},{6,7,11},
 {6,8,10},{6,9,12},{7,12,13},{10,11,5}}
 I={{0,6},{1,3},{2,11},{4,12},{7,10},{8,5},{9,13}}
 Examples of antimorphisms:
   C: \alpha=(0 9 3 12)(1 7 2 13)(4 6 10 11)(5 8)
      B_1={{0,3,4},{0,9,10},{1,7,9},{1,8,11},{1,12,5},{2,6,13},
      {2,9,5},{2,8,12},{3,10,12},{4,8,9},{4,11,13},{6,7,11},
      {6,8,10},{7,12,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 13 
 |Aut(T)|=4 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,12,13},{2,3,7},{2,4,10},{2,5,11},{2,9,13},{2,8,12},
 {3,6,13},{3,9,11},{3,10,12},{4,5,12},{4,7,13},{4,8,9},{5,7,10},{5,8,13},
 {6,7,11},{6,8,10},{6,9,12},{10,11,13}}
 I={{0,13},{1,10},{2,6},{3,8},{4,11},{5,9},{7,12}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 3 10 8)(2 7 9 4)(5 11 6 12)(13)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,4,6},{1,7,9},
      {2,4,10},{2,5,11},{2,9,13},{3,6,13},{5,7,10},{5,8,13},
      {6,8,10},{6,9,12}}
   C: \alpha=(0)(1 4 2 3 11 5)(6 10 7 9 8 12)(13)
      B_1={{0,1,2},{0,9,10},{0,11,12},{1,4,6},{1,8,11},{2,3,7},
      {2,5,11},{3,6,13},{3,10,12},{4,7,13},{4,8,9},{5,7,10},
      {5,8,13},{6,9,12}}
   D: \alpha=(0 13)(1)(2 12 6 7)(3 8)(4 9 11 5)(10)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,4,6},{1,8,11},{2,3,7},
      {2,5,11},{2,9,13},{3,6,13},{3,10,12},{4,8,9},{5,7,10},
      {5,8,13},{6,9,12}}
   E: \alpha=(0)(1 3 10 8)(2 4 9 7)(5 12 6 11)(13)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,4,6},{1,7,9},
      {1,12,13},{2,4,10},{2,5,11},{2,9,13},{5,7,10},{6,8,10},
      {6,9,12},{10,11,13}}
 # of antimorphisms of SASC-graph: 16 (fair: 12) 
 # of halving permutations: 8 (fair: 4; strong: 2) 


 Subsystem No. 14 
 |Aut(T)|=4 
 B={{0,1,2},{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,10},{2,5,11},{2,6,13},{2,8,12},
 {3,8,13},{3,9,11},{3,10,12},{4,5,12},{4,8,9},{4,11,13},{5,7,10},{5,9,13},
 {6,7,11},{6,8,10},{6,9,12},{7,12,13}}
 I={{0,13},{1,12},{2,9},{3,6},{4,7},{5,8},{10,11}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 3 10 8)(2 7 9 4)(5 12 6 11)(13)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,4,6},{1,7,9},
      {1,10,13},{2,4,10},{4,5,12},{4,11,13},{5,7,10},{6,7,11},
      {6,8,10},{7,12,13}}
   C: \alpha=(0)(1 3 9 4 10 8 2 7)(5 11 6 12)(13)
      B_1={{0,3,4},{0,7,8},{0,11,12},{1,3,5},{1,4,6},{1,10,13},
      {2,3,7},{2,5,11},{2,6,13},{4,8,9},{5,7,10},{5,9,13},
      {6,8,10},{6,9,12}}
   E: \alpha=(0)(1 3 10 8)(2 4 9 7)(5 12 6 11)(13)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,3,5},{1,4,6},{1,7,9},
      {1,10,13},{2,4,10},{2,5,11},{2,6,13},{5,7,10},{5,9,13},
      {6,8,10},{6,9,12}}
 # of antimorphisms of SASC-graph: 20 (fair: 8) 
 # of halving permutations: 14 (fair: 2; strong: 2) 


 System No. 75 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,12},
 {2,5,13},{2,6,11},{2,8,10},{2,9,0},{3,6,0},{3,8,13},{3,9,11},{3,10,12},
 {4,5,10},{4,7,0},{4,8,9},{4,11,13},{5,7,11},{5,8,0},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,0}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   A: \alpha=(0 2 8 13 1 7)(3 5 11 4 12 6)(9 10)
      B_1={{1,4,6},{1,7,9},{1,8,11},{1,12,0},{2,4,12},{2,9,0},
      {3,6,0},{3,8,13},{3,9,11},{4,8,9},{5,7,11},{5,8,0},
      {5,9,12},{6,9,13}}
   C: \alpha=(0)(1 5 11 9)(2 12 8 4 6 7 3 10)(13)
      B_1={{1,7,9},{1,10,13},{1,12,0},{2,4,12},{3,10,12},{4,5,10},
      {4,7,0},{4,8,9},{4,11,13},{5,7,11},{5,9,12},{6,7,10},
      {7,12,13},{10,11,0}}
 # of antimorphisms of SASC-graph: 10 (fair: 0) 
 # of halving permutations: 6 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,12},
 {2,5,13},{2,6,11},{2,8,10},{2,9,1},{3,6,1},{3,8,13},{3,9,11},{3,10,12},
 {4,5,10},{4,7,1},{4,8,9},{4,11,13},{5,7,11},{5,8,1},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,1}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   C: \alpha=(0 3 10 7 8 13)(1 4 5 11)(2 12 6 9)
      B_1={{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,8,10},
      {2,9,1},{3,10,12},{4,5,10},{4,8,9},{5,8,1},{5,9,12},
      {6,8,12},{10,11,1}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,13},{3,9,11},{3,10,12},
 {4,5,10},{4,7,2},{4,8,9},{4,11,13},{5,7,11},{5,8,2},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,2}}
 I={{0,1},{3,7},{4,12},{5,13},{6,11},{8,10},{9,2}}
 Examples of antimorphisms:
   C: \alpha=(0 2 10 7 13 11 6 3 12 4 1 5 9 8)
      B_1={{0,3,4},{0,7,8},{1,4,6},{1,8,11},{3,6,2},{3,8,13},
      {3,9,11},{4,5,10},{4,7,2},{5,7,11},{5,8,2},{5,9,12},
      {7,12,13},{10,11,2}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 3 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,3},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,3},{2,4,12},{2,5,13},{2,6,11},{2,8,10},{2,9,3},
 {4,5,10},{4,7,3},{4,8,9},{4,11,13},{5,7,11},{5,8,3},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,3}}
 I={{0,4},{1,5},{2,7},{6,3},{8,13},{9,11},{10,12}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=1 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,13},{2,6,11},{2,8,10},{2,9,4},
 {3,6,4},{3,8,13},{3,9,11},{3,10,12},{5,7,11},{5,8,4},{5,9,12},{6,7,10},
 {6,8,12},{6,9,13},{7,12,13},{10,11,4}}
 I={{0,3},{1,6},{2,12},{5,10},{7,4},{8,9},{11,13}}
 Examples of antimorphisms:
   C: \alpha=(0 12 10 13)(1 4 11 9 7 3)(2 5 6 8)
      B_1={{0,9,10},{0,13,4},{1,12,4},{2,3,7},{2,5,13},{2,9,4},
      {3,6,4},{3,8,13},{3,9,11},{3,10,12},{5,8,4},{5,9,12},
      {6,8,12},{6,9,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 76 
 |Aut(S)|=5 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,13},
 {2,5,10},{2,6,8},{2,9,12},{2,11,0},{3,6,0},{3,8,9},{3,10,12},{3,11,13},
 {4,5,12},{4,7,11},{4,8,10},{4,9,0},{5,7,13},{5,8,0},{5,9,11},{6,7,12},
 {6,9,13},{6,10,11},{7,10,0},{8,12,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,13},
 {2,5,10},{2,6,8},{2,9,12},{2,11,1},{3,6,1},{3,8,9},{3,10,12},{3,11,13},
 {4,5,12},{4,7,11},{4,8,10},{4,9,1},{5,7,13},{5,8,1},{5,9,11},{6,7,12},
 {6,9,13},{6,10,11},{7,10,1},{8,12,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   A: \alpha=(0 2 11)(1 12)(3 5)(4 6)(7 9)(8)(10 13)
      B_1={{0,3,4},{0,7,8},{0,13,1},{2,3,7},{2,4,13},{2,11,1},
      {3,6,1},{3,11,13},{4,7,11},{4,8,10},{4,9,1},{5,7,13},
      {5,8,1},{7,10,1}}
   B: \alpha=(0 2)(1 12)(3 5)(4 6)(7 9)(8)(10 13)(11)
      B_1={{0,3,4},{0,7,8},{0,11,12},{0,13,1},{2,3,7},{2,4,13},
      {3,6,1},{3,11,13},{4,7,11},{4,8,10},{4,9,1},{5,7,13},
      {5,8,1},{7,10,1}}
   C: \alpha=(0 2 11)(1 12)(3 10 7 6)(4 5 13 9)(8)
      B_1={{0,3,4},{0,7,8},{0,13,1},{2,3,7},{2,4,13},{2,11,1},
      {3,6,1},{3,8,9},{3,11,13},{4,7,11},{4,9,1},{5,7,13},
      {5,8,1},{7,10,1}}
 # of antimorphisms of SASC-graph: 9 (fair: 3) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,12},{3,11,13},
 {4,5,12},{4,7,11},{4,8,10},{4,9,2},{5,7,13},{5,8,2},{5,9,11},{6,7,12},
 {6,9,13},{6,10,11},{7,10,2},{8,12,13}}
 I={{0,1},{3,7},{4,13},{5,10},{6,8},{9,12},{11,2}}
 Examples of antimorphisms:
   C: \alpha=(0 1)(2 12 7 13)(3 4 6 5)(8 10 11 9)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},
      {3,6,2},{3,8,9},{3,10,12},{3,11,13},{6,7,12},{6,9,13},
      {6,10,11},{8,12,13}}
 # of antimorphisms of SASC-graph: 2 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 77 
 |Aut(S)|=3 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,13},
 {2,5,8},{2,6,12},{2,9,0},{2,10,11},{3,6,0},{3,8,9},{3,10,12},{3,11,13},
 {4,5,10},{4,7,12},{4,8,0},{4,9,11},{5,7,13},{5,9,12},{5,11,0},{6,7,11},
 {6,8,10},{6,9,13},{7,10,0},{8,12,13}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 12 7 5)(1 4 2 3)(6 13 11 8)(9 10)
      B_1={{1,3,5},{1,7,9},{1,8,11},{2,4,13},{2,6,12},{2,9,0},
      {3,6,0},{3,8,9},{4,7,12},{4,9,11},{5,9,12},{5,11,0},
      {6,7,11},{6,9,13}}
   C: \alpha=(0 5 7 12)(1 11 13 4)(2 6 8 3)(9 10)
      B_1={{1,8,11},{2,3,7},{2,4,13},{2,10,11},{3,6,0},{3,10,12},
      {4,5,10},{4,7,12},{4,8,0},{4,9,11},{5,11,0},{6,7,11},
      {6,8,10},{7,10,0}}
   D: \alpha=(0 5 7 12)(1 3 2 4)(6 8 11 13)(9 10)
      B_1={{1,3,5},{1,7,9},{1,8,11},{2,4,13},{2,6,12},{2,9,0},
      {3,6,0},{3,8,9},{4,7,12},{4,9,11},{5,9,12},{5,11,0},
      {6,7,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,13},
 {2,5,8},{2,6,12},{2,9,1},{2,10,11},{3,6,1},{3,8,9},{3,10,12},{3,11,13},
 {4,5,10},{4,7,12},{4,8,1},{4,9,11},{5,7,13},{5,9,12},{5,11,1},{6,7,11},
 {6,8,10},{6,9,13},{7,10,1},{8,12,13}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 2 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,2},{1,3,5},{1,4,6},
 {1,7,9},{1,8,11},{1,10,13},{1,12,2},{3,6,2},{3,8,9},{3,10,12},{3,11,13},
 {4,5,10},{4,7,12},{4,8,2},{4,9,11},{5,7,13},{5,9,12},{5,11,2},{6,7,11},
 {6,8,10},{6,9,13},{7,10,2},{8,12,13}}
 I={{0,1},{3,7},{4,13},{5,8},{6,12},{9,2},{10,11}}
 Examples of antimorphisms:
   B: \alpha=(0 6 8 11)(1 12 5 10)(2 9)(3)(4 13)(7)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,2},{1,3,5},
      {1,7,9},{1,8,11},{1,10,13},{3,8,9},{4,8,2},{5,7,13},
      {5,9,12},{8,12,13}}
   C: \alpha=(0 5 4 8 1 13)(2 6 12 9 11 10)(3 7)
      B_1={{0,7,8},{0,9,10},{0,13,2},{1,4,6},{1,7,9},{1,8,11},
      {4,5,10},{4,7,12},{5,7,13},{5,9,12},{6,7,11},{6,8,10},
      {6,9,13},{7,10,2}}
   D: \alpha=(0 11 8 6)(1 10 5 12)(2 9)(3)(4 13)(7)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,13,2},{1,3,5},
      {1,7,9},{1,8,11},{1,10,13},{3,8,9},{4,8,2},{5,7,13},
      {5,9,12},{8,12,13}}
 # of antimorphisms of SASC-graph: 4 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,13},{2,5,8},{2,6,12},{2,9,7},{2,10,11},
 {3,6,7},{3,8,9},{3,10,12},{3,11,13},{4,5,10},{4,8,7},{4,9,11},{5,9,12},
 {5,11,7},{6,8,10},{6,9,13},{8,12,13}}
 I={{0,8},{1,9},{2,3},{4,12},{5,13},{6,11},{10,7}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 8 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,8},{1,3,5},{1,4,6},
 {1,7,9},{1,10,13},{1,12,8},{2,3,7},{2,4,13},{2,6,12},{2,9,8},{2,10,11},
 {3,6,8},{3,10,12},{3,11,13},{4,5,10},{4,7,12},{4,9,11},{5,7,13},{5,9,12},
 {5,11,8},{6,7,11},{6,9,13},{7,10,8}}
 I={{0,7},{1,11},{2,5},{3,9},{4,8},{6,10},{12,13}}
 Examples of antimorphisms:
   A: \alpha=(0 4 1 5)(2 10 9 11 6 3 7 8)(12 13)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,4,6},{1,7,9},{2,3,7},
      {2,4,13},{2,6,12},{2,9,8},{4,7,12},{5,7,13},{5,9,12},
      {6,7,11},{6,9,13}}
   B: \alpha=(0 3 8 10)(1 11)(2)(4 6 7 9)(5)(12 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,8},{1,4,6},
      {1,7,9},{1,12,8},{2,6,12},{2,9,8},{4,7,12},{5,9,12},
      {5,11,8},{7,10,8}}
   C: \alpha=(0 4 1 5)(2 10 9 11 6 3 7 8)(12)(13)
      B_1={{0,1,2},{0,5,6},{0,9,10},{1,4,6},{1,7,9},{2,3,7},
      {2,4,13},{2,6,12},{2,9,8},{4,7,12},{5,7,13},{5,9,12},
      {6,7,11},{6,9,13}}
   D: \alpha=(0 10 8 3)(1 11)(2)(4 9 7 6)(5)(12 13)
      B_1={{0,1,2},{0,3,4},{0,5,6},{0,11,12},{0,13,8},{1,4,6},
      {1,7,9},{1,12,8},{2,6,12},{2,9,8},{4,7,12},{5,9,12},
      {5,11,8},{7,10,8}}
 # of antimorphisms of SASC-graph: 6 (fair: 2) 
 # of halving permutations: 3 (fair: 1; strong: 0) 


 System No. 78 
 |Aut(S)|=4 


 Subsystem No. 0 
 |Aut(T)|=1 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,10},
 {2,5,12},{2,6,8},{2,9,0},{2,11,13},{3,6,0},{3,8,10},{3,9,11},{3,12,13},
 {4,5,9},{4,7,12},{4,8,13},{4,11,0},{5,7,13},{5,8,0},{5,10,11},{6,7,11},
 {6,9,13},{6,10,12},{7,10,0},{8,9,12}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=1 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,10},
 {2,5,12},{2,6,8},{2,9,1},{2,11,13},{3,6,1},{3,8,10},{3,9,11},{3,12,13},
 {4,5,9},{4,7,12},{4,8,13},{4,11,1},{5,7,13},{5,8,1},{5,10,11},{6,7,11},
 {6,9,13},{6,10,12},{7,10,1},{8,9,12}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 # of antimorphisms of SASC-graph: 0 (fair: 0) 
 # of halving permutations: 0 (fair: 0; strong: 0) 


 Subsystem No. 4 
 |Aut(T)|=2 
 B={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},{1,3,5},{1,7,9},
 {1,8,11},{1,10,13},{1,12,4},{2,3,7},{2,5,12},{2,6,8},{2,9,4},{2,11,13},
 {3,6,4},{3,8,10},{3,9,11},{3,12,13},{5,7,13},{5,8,4},{5,10,11},{6,7,11},
 {6,9,13},{6,10,12},{7,10,4},{8,9,12}}
 I={{0,3},{1,6},{2,10},{5,9},{7,12},{8,13},{11,4}}
 Examples of antimorphisms:
   C: \alpha=(0 3)(1 4 10 5 12 7 11 2 6 13 8 9)
      B_1={{0,1,2},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,4},
      {1,8,11},{1,10,13},{1,12,4},{2,6,8},{5,10,11},{6,7,11},
      {6,10,12},{8,9,12}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 4 (fair: 0; strong: 0) 


 Subsystem No. 5 
 |Aut(T)|=4 
 B={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,11,12},{0,13,5},{1,4,6},{1,7,9},
 {1,8,11},{1,10,13},{1,12,5},{2,3,7},{2,4,10},{2,6,8},{2,9,5},{2,11,13},
 {3,6,5},{3,8,10},{3,9,11},{3,12,13},{4,7,12},{4,8,13},{4,11,5},{6,7,11},
 {6,9,13},{6,10,12},{7,10,5},{8,9,12}}
 I={{0,6},{1,3},{2,12},{4,9},{7,13},{8,5},{10,11}}
 Examples of antimorphisms:
   A: \alpha=(0 8 3 12)(1 5 10 13 6 2 11 7)(4 9)
      B_1={{0,11,12},{1,4,6},{1,8,11},{1,10,13},{1,12,5},{2,4,10},
      {2,6,8},{3,8,10},{4,7,12},{4,8,13},{4,11,5},{6,7,11},
      {6,10,12},{8,9,12}}
   B: \alpha=(0 8 3 12)(1 2 6 5)(4)(7 10 13 11)(9)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,13,5},{1,10,13},
      {2,3,7},{2,4,10},{2,9,5},{3,6,5},{3,9,11},{3,12,13},
      {4,11,5},{6,7,11}}
   C: \alpha=(0 8 3 12)(1 5 13 11 6 2 7 10)(4 9)
      B_1={{0,7,8},{1,4,6},{1,8,11},{1,12,5},{2,4,10},{2,6,8},
      {2,11,13},{3,12,13},{4,7,12},{4,8,13},{4,11,5},{6,10,12},
      {7,10,5},{8,9,12}}
   E: \alpha=(0 8 3 12)(1 2 6 5)(4 9)(7 10 13 11)
      B_1={{0,1,2},{0,3,4},{0,7,8},{0,9,10},{0,13,5},{1,4,6},
      {1,7,9},{1,10,13},{2,3,7},{3,6,5},{3,9,11},{3,12,13},
      {6,7,11},{6,9,13}}
 # of antimorphisms of SASC-graph: 22 (fair: 6) 
 # of halving permutations: 10 (fair: 2; strong: 2) 


 Subsystem No. 7 
 |Aut(T)|=1 
 B={{0,1,2},{0,3,4},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,3,5},{1,4,6},
 {1,8,11},{1,10,13},{1,12,7},{2,4,10},{2,5,12},{2,6,8},{2,9,7},{2,11,13},
 {3,6,7},{3,8,10},{3,9,11},{3,12,13},{4,5,9},{4,8,13},{4,11,7},{5,8,7},
 {5,10,11},{6,9,13},{6,10,12},{8,9,12}}
 I={{0,8},{1,9},{2,3},{4,12},{5,13},{6,11},{10,7}}
 Examples of antimorphisms:
   A: \alpha=(0 4 9 3 12 10)(1 13 6 7)(2 8 5 11)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,11,12},{0,13,7},{1,12,7},
      {2,5,12},{2,9,7},{2,11,13},{3,12,13},{4,5,9},{5,8,7},
      {6,9,13},{8,9,12}}
   C: \alpha=(0 1 5 6 4 12 7 8)(2 3)(9 10 13 11)
      B_1={{0,1,2},{0,5,6},{0,9,10},{0,13,7},{1,12,7},{2,4,10},
      {2,5,12},{2,6,8},{2,9,7},{2,11,13},{4,5,9},{4,8,13},
      {4,11,7},{5,10,11}}
 # of antimorphisms of SASC-graph: 4 (fair: 0) 
 # of halving permutations: 2 (fair: 0; strong: 0) 


 System No. 79 
 |Aut(S)|=36 


 Subsystem No. 0 
 |Aut(T)|=6 
 B={{1,3,5},{1,4,6},{1,7,9},{1,8,11},{1,10,13},{1,12,0},{2,3,7},{2,4,9},
 {2,5,0},{2,6,12},{2,8,10},{2,11,13},{3,6,10},{3,8,0},{3,9,11},{3,12,13},
 {4,5,8},{4,7,13},{4,10,12},{4,11,0},{5,7,12},{5,9,13},{5,10,11},{6,7,11},
 {6,8,13},{6,9,0},{7,10,0},{8,9,12}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 3 11 13 4 12)(1 8 9 2 7 10)(5)(6)
      B_1={{1,3,5},{1,7,9},{1,10,13},{1,12,0},{2,3,7},{2,6,12},
      {3,6,10},{3,9,11},{3,12,13},{4,7,13},{5,7,12},{5,9,13},
      {6,8,13},{8,9,12}}
   C: \alpha=(0 1 3 10)(2 4 7 12)(5 6)(8 11 9 13)
      B_1={{1,3,5},{1,7,9},{1,8,11},{1,10,13},{2,3,7},{2,4,9},
      {2,5,0},{2,8,10},{4,5,8},{5,7,12},{5,9,13},{5,10,11},
      {7,10,0},{8,9,12}}
 # of antimorphisms of SASC-graph: 27 (fair: 3) 
 # of halving permutations: 24 (fair: 0; strong: 0) 


 Subsystem No. 1 
 |Aut(T)|=4 
 B={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},{2,3,7},{2,4,9},
 {2,5,1},{2,6,12},{2,8,10},{2,11,13},{3,6,10},{3,8,1},{3,9,11},{3,12,13},
 {4,5,8},{4,7,13},{4,10,12},{4,11,1},{5,7,12},{5,9,13},{5,10,11},{6,7,11},
 {6,8,13},{6,9,1},{7,10,1},{8,9,12}}
 I={{0,2},{3,5},{4,6},{7,9},{8,11},{10,13},{12,1}}
 Examples of antimorphisms:
   B: \alpha=(0)(1 7 12 9)(2)(3 11 4 13)(5 8 6 10)
      B_1={{0,3,4},{0,7,8},{0,9,10},{2,3,7},{2,4,9},{2,8,10},
      {3,6,10},{3,8,1},{3,9,11},{4,5,8},{4,7,13},{4,10,12},
      {5,7,12},{6,9,1}}
   C: \alpha=(0 2)(1 7 5 10 12 9 6 8)(3 11 4 13)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {3,12,13},{4,11,1},{5,9,13},{5,10,11},{6,7,11},{6,8,13},
      {7,10,1},{8,9,12}}
   E: \alpha=(0 2)(1 7 12 9)(3 11 4 13)(5 8 6 10)
      B_1={{0,3,4},{0,5,6},{0,7,8},{0,9,10},{0,11,12},{0,13,1},
      {3,6,10},{3,8,1},{3,9,11},{4,5,8},{4,7,13},{4,10,12},
      {5,7,12},{6,9,1}}
 # of antimorphisms of SASC-graph: 12 (fair: 8) 
 # of halving permutations: 6 (fair: 2; strong: 2) 


 System No. 80 
 |Aut(S)|=60 


 Subsystem No. 0 
 |Aut(T)|=4 
 B={{1,3,5},{1,4,7},{1,6,8},{1,9,11},{1,10,13},{1,12,0},{2,3,9},{2,4,6},
 {2,5,10},{2,7,0},{2,8,12},{2,11,13},{3,6,11},{3,7,12},{3,8,13},{3,10,0},
 {4,5,13},{4,8,9},{4,10,12},{4,11,0},{5,7,11},{5,8,0},{5,9,12},{6,7,10},
 {6,9,0},{6,12,13},{7,9,13},{8,10,11}}
 I={{1,2},{3,4},{5,6},{7,8},{9,10},{11,12},{13,0}}
 Examples of antimorphisms:
   B: \alpha=(0 3 12 5)(1)(2)(4 11 6 13)(7 10 8 9)
      B_1={{1,3,5},{1,4,7},{1,6,8},{2,3,9},{2,4,6},{2,5,10},
      {3,6,11},{3,10,0},{4,5,13},{4,8,9},{4,10,12},{5,9,12},
      {6,7,10},{6,9,0}}
   C: \alpha=(0)(1 2)(3 4 10 11 5 9 7 12 8 6 13)
      B_1={{2,3,9},{2,4,6},{2,5,10},{2,7,0},{2,8,12},{2,11,13},
      {3,6,11},{3,10,0},{4,8,9},{4,10,12},{5,7,11},{5,8,0},
      {6,12,13},{7,9,13}}
   E: \alpha=(0 3 12 5)(1)(2)(4 11 6 13)(7 9 8 10)
      B_1={{1,3,5},{1,4,7},{1,6,8},{2,3,9},{2,4,6},{2,5,10},
      {3,6,11},{3,7,12},{3,8,13},{4,5,13},{4,8,9},{5,7,11},
      {5,8,0},{6,7,10}}
 # of antimorphisms of SASC-graph: 28 (fair: 10) 
 # of halving permutations: 20 (fair: 2; strong: 2)