lower bound = 57

C(12,4,3) = 57

Method of Construction: simple construction: induced on c(13,5,4) covering

Lower Bound: Schonheim

  1  2  3  7
  1  2  5  6
  1  2  4  8
  1  2  9 12
  1  2 10 11
  1  3  5  9
  1  3  6  8
  1  3 10 12
  1  3  4 11
  1  5  6 11
  1  5  6 12
  1  5  7  8
  1  4  5 10
  1  6  7 10
  9 10 11 12
  4  8 10 11
  4  7  9 10
  4  7  8 12
  4  6 11 12
  6  8 10 12
  6  7  9 12
  6  7  8 11
  4  5  9 12
  5  8  9 11
  4  5  7 11
  5  7 10 12
  5  6  9 10
  4  5  6  8
  1  4  6  9
  1  7  9 11
  1  4  7 12
  1  8  9 10
  1  8 11 12
  2  3  4  5
  2  3  6 12
  2  3  8 11
  2  3  9 10
  2  5  7  9
  2  5  8 12
  2  5 10 11
  2  4  6  7
  2  6  8  9
  2  6 10 11
  2  7  8 10
  3  4  8  9
  3  8  9 12
  3  4  7 12
  3  7 10 11
  3  7  8  9
  3  4  6 10
  3  6  9 11
  3  5 11 12
  3  5  8 10
  3  5  6  7
  2  7 11 12
  2  4  9 11
  2  4 10 12