C(31,6,2) = 31
Method of Construction: cyclic covering found by a search program
Lower Bound: Schonheim
2 3 5 10 14 20
3 4 6 11 15 21
4 5 7 12 16 22
5 6 8 13 17 23
6 7 9 14 18 24
7 8 10 15 19 25
8 9 11 16 20 26
9 10 12 17 21 27
10 11 13 18 22 28
11 12 14 19 23 29
12 13 15 20 24 30
13 14 16 21 25 31
1 14 15 17 22 26
2 15 16 18 23 27
3 16 17 19 24 28
4 17 18 20 25 29
5 18 19 21 26 30
6 19 20 22 27 31
1 7 20 21 23 28
2 8 21 22 24 29
3 9 22 23 25 30
4 10 23 24 26 31
1 5 11 24 25 27
2 6 12 25 26 28
3 7 13 26 27 29
4 8 14 27 28 30
5 9 15 28 29 31
1 6 10 16 29 30
2 7 11 17 30 31
1 3 8 12 18 31
1 2 4 9 13 19