C(17,4,2) <=26

Method of construction: colex greedy covering

 1  2  3  4
 1  5  6  7
 2  5  8  9
 3  6  8 10
 4  7  9 10
 3  5 11 12
 2  6 11 13
 1  8 12 13
 4  8 11 14
 2  7 12 14
 3  9 13 14
 1  9 11 15
 4  6 12 15
 5 10 13 15
 1 10 14 16
 3  7 15 16
 4  5 16 17
 6  9 12 16
 7  8 11 17
 2 10 12 17
 6 14 15 17
 2  8 15 16
 4  7 13 16
 1  3  9 17
 5 10 11 14
11 13 16 17