C(17,5,2) <=16

Method of construction: random greedy covering

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