C(15,5,2) <=13

Method of construction: random greedy covering

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