k4_g4 := List([1..16], i -> []);

k4_g4[8,1] := [ [ 2, 4, 6, 8 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 1, 3, 5, 7 ] ];

k4_g4[10,1] := [ [ 2, 4, 8, 10 ], [ 1, 3, 5, 9 ], [ 2, 4, 6, 10 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 3, 5, 7, 9 ], [ 4, 6, 8, 10 ], [ 1, 5, 7, 9 ], [ 2, 6, 8, 10 ], [ 1, 3, 7, 9 ] ];

k4_g4[11,1] := [ [ 2, 4, 9, 11 ], [ 1, 3, 5, 10 ], [ 2, 4, 6, 11 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 3, 5, 7, 9 ], [ 4, 6, 8, 10 ], [ 5, 7, 9, 11 ], [ 1, 6, 8, 10 ], [ 2, 7, 9, 11 ], [ 1, 3, 8, 10 ] ];

k4_g4[12,1] := [ [ 2, 4, 10, 12 ], [ 1, 3, 5, 11 ], [ 2, 4, 6, 12 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 3, 5, 7, 9 ], [ 4, 6, 8, 10 ], [ 5, 7, 9, 11 ], [ 6, 8, 10, 12 ], [ 1, 7, 9, 11 ], [ 2, 8, 10, 12 ], [ 1, 3, 9, 11 ] ];

k4_g4[13,1] := [ [ 2, 4, 11, 13 ], [ 1, 3, 5, 12 ], [ 2, 4, 6, 13 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 3, 5, 7, 9 ], [ 4, 6, 8, 10 ], 
  [ 5, 7, 9, 11 ], [ 6, 8, 10, 12 ], [ 7, 9, 11, 13 ], [ 1, 8, 10, 12 ], [ 2, 9, 11, 13 ], [ 1, 3, 10, 12 ] ];

k4_g4[14,1] := [ [ 2, 4, 12, 14 ], [ 1, 3, 5, 13 ], [ 2, 4, 6, 14 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 3, 5, 7, 9 ], [ 4, 6, 8, 10 ], 
  [ 5, 7, 9, 11 ], [ 6, 8, 10, 12 ], [ 7, 9, 11, 13 ], [ 8, 10, 12, 14 ], [ 1, 9, 11, 13 ], [ 2, 10, 12, 14 ], [ 1, 3, 11, 13 ] ];

k4_g4[15,1] := [ [ 2, 4, 13, 15 ], [ 1, 3, 5, 14 ], [ 2, 4, 6, 15 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 3, 5, 7, 9 ], [ 4, 6, 8, 10 ], 
  [ 5, 7, 9, 11 ], [ 6, 8, 10, 12 ], [ 7, 9, 11, 13 ], [ 8, 10, 12, 14 ], [ 9, 11, 13, 15 ], [ 1, 10, 12, 14 ], [ 2, 11, 13, 15 ], [ 1, 3, 12, 14 ] ];

k4_g4[16,1] := [ [ 2, 4, 14, 16 ], [ 1, 3, 5, 15 ], [ 2, 4, 6, 16 ], [ 1, 3, 5, 7 ], [ 2, 4, 6, 8 ], [ 3, 5, 7, 9 ], [ 4, 6, 8, 10 ], 
  [ 5, 7, 9, 11 ], [ 6, 8, 10, 12 ], [ 7, 9, 11, 13 ], [ 8, 10, 12, 14 ], [ 9, 11, 13, 15 ], [ 10, 12, 14, 16 ], [ 1, 11, 13, 15 ], [ 2, 12, 14, 16 ], [ 1, 3, 13, 15 ] ];