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