C(13,4,2) <=13

Method of construction: cyclic covering found by a search program

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