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Packing designs with block size 6 and index 5

✍ Scribed by Ahmed M. Assaf; Alan Hartman; N. Shalaby

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 473 KB
Volume: 103
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90262-e

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✦ Synopsis

A (v, K, A) packing design of order v, block size K and index 1 is a collection of K-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most I blocks. The packing problem is to determine the maximum number of blocks in a packing design. The only previous work on the packing problem with K = 6 concerns itself with the cases where the maximum packing design is in fact a balanced incomplete block design. In this paper we solve the packing problem with K = 6 and A = 5 and all positive integers v with the possible exceptions of v = 41, 47, 53, 59, 62, 71.

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