C(16,5,2) <=15

Method of construction: random greedy covering

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