lower bound = 26

C(31,7,2) = 26

Method of Construction: communicated by d. todorov, using pg(2,4)

Lower Bound: Handbook of Combinatorial Designs section on coverings

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