C(14,7,2) <=6

Method of construction: simulated annealing covering

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