lower bound = 31

C(30,6,2) = 31

Method of Construction: simple construction: deleted element from c(v+1,k,t) covering

Lower Bound: Handbook of Combinatorial Designs section on coverings

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