C(15,4,2) <=19

Method of construction: random greedy covering

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