C(19,3,2) <=57

Method of construction: simple construction: induced on c(20,4,3) covering

10 12 16
10 13 18
 1 11 12
11 13 19
12 14 17
 1 13 17
14 15 19
 1 15 18
17 18 19
 2 10 11
 2 12 13
 2 14 18
 2 16 19
 2  3  5
 1  2  4
 2  6  8
 2  7 15
 2  9 17
 3 13 15
 3 16 17
 1  3 19
 3  4 18
 3  6 10
 3  7 12
 3  8 14
 3  9 11
 4 10 14
 4 11 15
 4 13 16
 4  5 17
 4  6  7
 4  8 19
 4  9 12
 5 10 19
 5 11 14
 5 12 15
 5 16 18
 5  6 13
 1  5  7
 5  8  9
 6 11 16
 6 12 19
 1  6 14
 6 15 17
 6  9 18
 7 10 17
 7 11 18
 7 14 16
 7  8 13
 7  9 19
 8 10 15
 8 11 17
 8 12 18
 1  8 16
 1  9 10
 9 13 14
 9 15 16