C(16,4,2) <=20

Method of construction: simple construction: induced on c(17,5,3) covering

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