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

  • Authors:

  • Rudolf Mathon;Anne Penfold Street

  • Affiliations:

  • Department of Computer Science, University of Toronto, Toronto, Ont., Canada M5S 1A4;Centre for Discrete Mathematics and Computing, The University of Queensland, Brisbane 4072, Australia

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2002

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Abstract

We 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.