C(11,3,2) = 19

Method of Construction: random greedy covering

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