lower bound = 24

24 ≤ CC(30,7,2) ≤ 25

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

Lower Bound: Horsley, Theorem 14c, r=5, d=1

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