On resolvable designs \(S_ 3(3;4,v)\). (English) Zbl 0648.05007

Jungnickel, Dieter; Vanstone, Scott A.

J. Comb. Theory, Ser. A 43, 334-337 (1986).

We study a method of Lonz and Vanstone which constructs an \(S_ 3(3,4,2n)\) from any given 1-factorization of \(K_{2n}\). We show that the resulting designs admit at least 3 mutually orthogonal resolutions whenever \(n\geq 4\) is even. In particular, the necessary conditions for the existence of a resolvable \(S_ 3(3,4,v)\) are also sufficient. Examples without repeated blocks are shown to exist provided that \(n\not\equiv 2\) mod 3.

MSC:

05B05	Combinatorial aspects of block designs
05C70	Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)

Keywords:

resolvability; designs; mutually orthogonal resolutions

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