C(17,3,2) <=46

Method of construction: random greedy covering

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