Construction of two non-isomorphic (11, 55, 20, 4, 6) Balanced Incomplete Block Designs having the same automorphism group

Abstract

A simple combinatorial problem derived from a configuration in PSL (2, 11) has two solutions. One can look at these solutions from different points of view. Interpreted as involutions, the first solution generates A 12and the second one M 12. Another interpretation produces two non-isomorphic (11, 55, 20, 4, 6) Balanced Incomplete Block Designs having the same automorphism group. (The existence of at least one (11, 55, 20, 4, 6) BIBD is mentioned in the tables of [7].)