Overlarge sets of 2-(11,5,2) designs and related configurations

AbstractWe consider the construction of several configurations, including: •overlarge sets of 2-(11,5,2) designs, that is, partitions of the set of all 5-subsets of a 12-set into 72 2-(11,5,2) designs;•an indecomposable doubly overlarge set of 2-(11,5,2) designs, that is, a partition of two copies of the set of all 5-subsets of a 12-set into 144 2-(11,5,2) designs, such that the 144 designs can be arranged into a 12×12 square with interesting row and column properties;•a partition of the Steiner system S(5,6,12) into 12 disjoint 2-(11,6,3) designs arising from the diagonal of the square;•bidistant permutation arrays and generalized Room squares arising from the doubly overlarge set, and their relation to some new strongly regular graphs