lower bound = 57

C(19,3,2) = 57

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

Lower Bound: Schonheim

 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