Abstract
Two Steiner triple systems (STS) are orthogonal if their sets of triples are disjoint, and two disjoint pairs of points defining intersecting triples in one system fail to do so in the other. We define the quantity σ (n) as the size of a maximum collection of pairwise orthogonal STS of order n. Special starters in the finite fields are used to improve the best known lower bounds on σ (n) for prime-powers n ≡ 1 (mod 6), n < 500. Additionally, hill-climbing and isomorphisms are used together to show σ (n) ≥ 3 or 4 for certain other small n, including some orders n ≡ 3 (mod 6). Asymptotic existence for three mutually orthogonal STS is a consequence.
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© 2003 Kluwer Academic Publishers
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Dinitz, J.H., Dukes, P. (2003). New Lower Bounds on the Maximum Number of Mutually Orthogonal Steiner Triple Systems. In: Wallis, W.D. (eds) Designs 2002. Mathematics and Its Applications, vol 563. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0245-2_5
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DOI: https://doi.org/10.1007/978-1-4613-0245-2_5
Publisher Name: Springer, Boston, MA
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