lower bound = 17

C(21,6,2) = 17

Method of Construction: simple construction: induced on c(22,7,3) covering

Lower Bound: Handbook of Combinatorial Designs section on coverings

  4 10 13 18 20 21
  3  5  7  9 20 21
  1  8 12 17 19 21
  2  5 11 16 17 21
  3  6 14 15 17 21
  8 11 15 18 19 20
  1  3  6 16 18 20
  2  5 12 14 18 20
  2  3 10 14 17 20
  4  8 13 14 16 19
  3  5  6  8 10 19
  2  6  7  8  9 19
  4  7  9 13 17 18
  7  9 10 12 15 16
  1  2  4  5 13 15
  1  7  9 10 11 14
  3  4  6 11 12 13