lower bound = 50

C(31,5,2) = 50

Method of Construction: covering pairs by quints, mullin, jcmcc 2:133-146, 1987

Lower Bound: Schonheim

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