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New coverings of t-sets with (t + 1)-sets

✍ Scribed by Kari J. Nurmela; Patric R. J. Östergård

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
434 KB
Volume
7
Category
Article
ISSN
1063-8539

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✦ Synopsis

The minimum number of k-subsets out of a v-set such that each t-set is contained in at least one k-set is denoted by C(v, k, t). In this article, a computer search for finding good such covering designs, leading to new upper bounds on C(v, k, t), is considered. The search is facilitated by predetermining automorphisms of desired covering designs. A stochastic heuristic search (embedded in the general framework of tabu search) is then used to find appropriate sets of orbits. A table of upper bounds on C(v, t + 1, t) for v ≤ 28 and t ≤ 8 is given, and the new covering designs are listed.

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