C(15,8,3) = 13

Method of Construction: covering provided by konstantin katskov, found by exhaustive search

Lower Bound: Handbook of Combinatorial Designs section on coverings

  1  2  3  4  5  6  7  8
  1  2  4  6 10 11 12 13
  1  2  9 11 12 13 14 15
  1  3  4  6  8  9 12 13
  1  3  5  7  8 11 12 13
  1  3  5  7  9 10 14 15
  1  4  6  8 10 11 14 15
  2  3  4  6  9 11 14 15
  2  3  8 10 12 13 14 15
  2  5  7  8  9 10 12 13
  2  5  7  8  9 11 14 15
  3  4  5  6  7  9 10 11
  4  5  6  7 12 13 14 15