12 ≤ C(30,16,3) ≤ 13

Method of Construction: simple construction: multiple of smaller covering

Lower Bound: Schonheim

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