24 ≤ C(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