C(28,4,2) <=63

Method of construction: simple construction: induced on c(29,5,3) covering

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