Overlarge sets of 2-(11, 5, 2) designs and related configurations (Q1849899)

This paper discusses the construction of mainly the following configurations: overlarge sets of \(2\)-\((11, 5, 2)\) designs; an indecomposable doubly overlarge set of \(2\)-\((11, 5, 2)\) designs; 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 from the doubly overlarge set, and their relation to some new strongly regular graphs. Tables have been provided of the parameters for which the existence of a strongly regular graph is known.