lower bound = 12

C(7,4,3) = 12

Method of Construction: simple construction: combined c(v-1,k,t) and c(v-1,k-1,t-1)

Lower Bound: Handbook of Combinatorial Designs section on coverings

  1  3  4  5
  1  2  3  6
  1  2  5  6
  3  4  5  6
  2  3  4  5
  1  2  4  6
  3  4  5  7
  1  5  6  7
  2  3  6  7
  2  4  6  7
  1  2  5  7
  1  3  4  7