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All 80 steiner triple systems on 15 elements are derived

✍ Scribed by Immo Diener; Eberhard Schmitt; Hans Ludwig de Vries

Publisher: Elsevier Science
Year: 1985
Tongue: English
Weight: 401 KB
Volume: 55
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(85)80017-0

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✦ Synopsis

We settle the remaining fourteen cases by exhibiting quadruple systems SQS(l6) that contain the triple systems STS(15) in question and briefly describe the techniques used to construct these systems. We also state some further computational results that we obtained as a by-product.

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Subsets of a v-set are in one-to-one correspondence with vertices of a v-dimensional unit cube, a Delaunay polytope of the lattice Z v . All vertices of the same cardinality k generate a (v -1)-dimensional root lattice Av-1 and are vertices of the Delaunay polytope P(v; k) of the lattice Av-1. Hence