C(19,8,3) <=27

Method of construction: simple construction: induced on c(20,9,4) covering

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