C(31,12,2) = 10

Method of Construction: lexicographic greedy covering

Lower Bound: Bounds for fixed number of blocks

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