lower bound = 48

C(30,5,2) = 48

Method of Construction: simple construction: induced on c(31,6,3) covering

Lower Bound: Schonheim

 15 16 18 22 30
 14 17 21 29 30
 13 16 20 28 29
 12 19 27 28 30
 11 18 26 27 29
 10 17 25 26 28
 10 11 15 20 23
  9 16 24 25 27
  9 10 14 19 22
  8 23 24 26 30
  8  9 13 18 21
  7 22 23 25 29
  7  9 15 21 26
  7  8 12 17 20
  6 21 22 24 28
  6 13 15 17 27
  6  8 14 20 25
  6  7 11 16 19
  5 20 21 23 27
  5 12 14 16 26
  5  7 13 19 24
  5  6 10 18 30
  4 19 20 22 26
  4 14 15 24 27
  4 11 13 25 30
  4  6 12 18 23
  4  5  9 17 29
  3 18 19 21 25
  3 13 14 23 26
  3 10 12 24 29
  3  6  9 12 15
  3  5 11 17 22
  3  4  8 16 28
  2 17 18 20 24
  2 12 13 22 25
  2  9 11 23 28
  2  8 15 19 29
  2  5  8 11 14
  2  4 10 16 21
  2  3  7 27 30
  1 16 17 19 23
  1 11 12 21 24
  1  8 10 22 27
  1  7 14 18 28
  1  5 15 25 28
  1  4  7 10 13
  1  3  9 20 30
  1  2  6 26 29