14 ≤ C(18,9,3) ≤ 16

Method of Construction: random greedy covering

Lower Bound: Schonheim

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