C(31,10,2) = 13

Method of Construction: simple construction: induced on c(32,11,3) covering

Lower Bound: Schonheim

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