C(17,6,2) <=12

Method of construction: lex covering

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