On resolvable designs

doi:10.1016/j.disc.2006.03.008

Discrete Mathematics

Volume 306, Issues 10–11, 28 May 2006, Pages 876-885

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Abstract

A balanced incomplete block design (BIBD) $B [k, λ; υ]$ is an arrangement of $υ$ elements in blocks of k elements each, such that every pair of elements is contained in exactly $λ$ blocks. A BIBD $B [k, 1; υ]$ is called resolvable if the blocks can be petitioned into $(υ - 1) / (k - 1)$ families each consisting of $υ / k$ mutually disjoint blocks. Ray-Chaudhuri and Wilson [8] proved the existence of resolvable BIBD's $B [3, 1; υ]$ for every $υ \equiv 3$ (mod 6). In addition to this result the existence is proved here of resolvable BIBD's $B [4, 1, υ]$ for every $υ \equiv 4$ (mod 12).

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: DOI of the original article: 10.1016/0012-365X(72)90091-X

: The original article was published in Discrete Mathematics 3 (1972) 343–357