lower bound = 78

C(31,4,2) = 78

Method of Construction: covering pairs by quads: mills, jcta 15:138-166, 1973.

Lower Bound: Schonheim

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