Another Look at Large Sets of Steiner Triple Systems

Martin J. Sharry and Anne Penfold Street
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Martin J. Sharry: The University of Queensland, Centre for Combinatorics, Department of Mathematics
Anne Penfold Street: The University of Queensland, Centre for Combinatorics, Department of Mathematics

Chapter Chapter 10 in Computational and Constructive Design Theory, 1996, pp 255-335 from Springer

Abstract: Abstract If v = 1 or 3 mod 6 and v > 7, then there exists a large set of Steiner triple systems of order v, LS (STS (v)). This result was largely known by 1984, though the six cases which were unsettled then have since been solved, and the proof simplified. The proof is by construction, using a fairly small number of initial large sets. Each construction is explained, often with the aid of tables of blocks. In the interests of brevity, proofs and complete examples are not given, though the ingredients needed for the construction of the examples are. The recursive constructions are of three types: (i) extension of a large set of STS (v) to a large set of STS (3v) by using idempotent commutative quasigroups; (ii) extension of a large set of STS (v)to a large set of STS (2v + 1) by using good one-factorizations; (iii) special constructions to fill in the remaining cases.

Keywords: Triple System; Counting Argument; Steiner Triple System; Balance Incomplete Block Design; Transversal Design (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4757-2497-4_10

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