C(11,4,2) <=11

Method of construction: cyclic covering found by a search program

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