17 ≤ C(40,18,3) ≤ 21

Created by: LJCR

Method of Construction: Multiple of (20,9,3) covering

Lower Bound: Horsley-Singh, Theorem 6, s=1

  1  2  3  6  7 10 17 19 20 21 22 23 26 27 30 37 39 40
  1  2  4  5  6  8 11 12 13 21 22 24 25 26 28 31 32 33
  1  2  4  7  9 10 11 14 16 21 22 24 27 29 30 31 34 36
  1  2  6  9 14 15 16 17 18 21 22 26 29 34 35 36 37 38
  1  3  4  8 13 14 15 17 20 21 23 24 28 33 34 35 37 40
  1  3  5  9 11 12 17 18 20 21 23 25 29 31 32 37 38 40
  1  3 10 11 12 13 15 16 19 21 23 30 31 32 33 35 36 39
  1  4  5  7  8 10 16 18 20 21 24 25 27 28 30 36 38 40
  1  4  5  7 12 14 15 17 19 21 24 25 27 32 34 35 37 39
  1  7  8  9 11 13 17 18 19 21 27 28 29 31 33 37 38 39
  2  3  4  7 11 16 17 19 20 22 23 24 27 31 36 37 39 40
  2  3  4 10 12 13 15 18 19 22 23 24 30 32 33 35 38 39
  2  3  5  8  9 10 14 15 19 22 23 25 28 29 30 34 35 39
  2  5  6  8 10 12 13 16 17 22 25 26 28 30 32 33 36 37
  2  5  7  8 10 11 15 18 20 22 25 27 28 30 31 35 38 40
  2  7  9 10 12 13 14 15 20 22 27 29 30 32 33 34 35 40
  3  4  5  6  7  9 13 15 16 23 24 25 26 27 29 33 35 36
  3  6  7  8 11 12 14 16 18 23 26 27 28 31 32 34 36 38
  4  6  8  9 12 15 16 19 20 24 26 28 29 32 35 36 39 40
  4  6  9 10 11 14 15 17 18 24 26 29 30 31 34 35 37 38
  5  6 11 13 14 16 18 19 20 25 26 31 33 34 36 38 39 40