C(30,3,2) = 150

Method of Construction: simple construction: induced on c(31,4,3) covering

Lower Bound: Schonheim

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