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

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