C(31,5,2) = 50
Method of Construction: covering pairs by quints, mullin, jcmcc 2:133-146, 1987
Lower Bound: Schonheim
1 9 11 14 17
1 2 10 12 18
2 3 11 13 19
3 4 12 14 20
1 4 5 13 21
2 5 6 14 22
1 3 6 7 23
2 4 7 8 24
3 5 8 9 25
4 6 9 10 26
5 7 10 11 27
6 8 11 12 28
7 9 12 13 15
8 10 13 14 16
2 15 17 25 26
3 16 18 26 27
4 17 19 27 28
5 15 18 20 28
6 15 16 19 21
7 16 17 20 22
8 17 18 21 23
9 18 19 22 24
10 19 20 23 25
11 20 21 24 26
12 21 22 25 27
13 22 23 26 28
14 15 23 24 27
1 16 24 25 28
1 8 19 20 29
2 9 20 21 30
3 10 21 22 29
4 11 22 23 30
5 12 23 24 29
6 13 24 25 30
7 14 25 26 29
1 8 26 27 30
2 9 27 28 29
3 10 15 28 30
4 11 15 16 29
5 12 16 17 30
6 13 17 18 29
7 14 18 19 30
1 8 15 22 31
2 9 16 23 31
3 10 17 24 31
4 11 18 25 31
5 12 19 26 31
6 13 20 27 31
7 14 21 28 31
1 2 29 30 31