C(14,4,3) <=91

Method of construction: steiner system, taken from hanani, canadian j. math, 12 (1960) pg. 154

 1  2  5 14
 1  3 11 14
 1  4  6 14
 1  7  8 14
 1  9 13 14
 1 10 12 14
 2  3  4 14
 2  6  8 14
 2  7  9 14
 2 10 13 14
 2 11 12 14
 3  5  6 14
 3  7 12 14
 3  8 13 14
 3  9 10 14
 4  5  9 14
 4  7 11 14
 4  8 10 14
 4 12 13 14
 5  7 13 14
 5  8 12 14
 5 10 11 14
 6  7 10 14
 6  9 12 14
 6 11 13 14
 8  9 11 14
 1  2  3  6
 1  2  4  7
 1  2  8 11
 1  2  9 10
 1  2 12 13
 1  3  4  5
 1  3  7 13
 1  3  8 10
 1  3  9 12
 1  4  8 12
 1  4  9 11
 1  4 10 13
 1  5  6 10
 1  5  7 12
 1  5  8  9
 1  5 11 13
 1  6  7  9
 1  6  8 13
 1  6 11 12
 1  7 10 11
 2  3  5 13
 2  3  7 10
 2  3  8 12
 2  3  9 11
 2  4  5  6
 2  4  8  9
 2  4 10 12
 2  4 11 13
 2  5  7 11
 2  5  8 10
 2  5  9 12
 2  6  7 12
 2  6  9 13
 2  6 10 11
 2  7  8 13
 3  4  6 12
 3  4  7  8
 3  4  9 13
 3  4 10 11
 3  5  7  9
 3  5  8 11
 3  5 10 12
 3  6  7 11
 3  6  8  9
 3  6 10 13
 3 11 12 13
 4  5  7 10
 4  5  8 13
 4  5 11 12
 4  6  7 13
 4  6  8 11
 4  6  9 10
 4  7  9 12
 5  6  7  8
 5  6  9 11
 5  6 12 13
 5  9 10 13
 6  8 10 12
 7  8  9 10
 7  8 11 12
 7  9 11 13
 7 10 12 13
 8  9 12 13
 8 10 11 13
 9 10 11 12