C(31,15,3) = 15

Method of Construction: simple construction: added element to c(v-1,k-1,t) covering

Lower Bound: Schonheim

  5  7  8  9 11 12 13 15 19 20 24 25 26 28 31
  3  9 10 12 13 14 19 21 22 25 26 27 29 30 31
  2  6 13 14 15 17 18 20 21 24 26 28 29 30 31
  1  5  6  7  9 10 18 22 23 24 25 28 29 30 31
  2  3  5  6  7  8 10 11 13 17 18 22 26 27 31
  1  2  3  5  7 12 15 17 19 20 23 27 29 30 31
  1  3  4 10 13 15 16 20 22 23 24 26 27 28 31
  3  4  6  8 11 12 16 18 19 24 27 28 29 30 31
  4  5  6  7 10 12 14 15 16 18 19 20 21 22 31
  2  3  4  5  7  9 14 16 17 21 24 25 27 28 31
  1  4  5  7  8 11 13 14 16 21 23 26 29 30 31
  1  3  6  8  9 11 14 15 18 20 21 23 25 27 31
  1  2  8 10 11 12 14 17 19 21 22 23 24 28 31
  2  4  8  9 10 11 15 16 17 20 22 25 29 30 31
  1  2  4  6  9 12 13 16 17 18 19 23 25 26 31