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# Equitable resolvable coverings

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## Abstract

In an earlier article, Willem H. Haemers has determined the minimum number of parallel classes in a resolvable 2-(qk,k,1) covering for all k ≥ 2 and q = 2 or 3. Here, we complete the case q = 4, by construction of the desired coverings using the method of simulated annealing. Secondly, we look at equitable resolvable 2-(qk,k,1) coverings. These are resolvable coverings which have the additional property that every pair of points is covered at most twice. We show that these coverings satisfy k < 2q −  , and we give several examples. In one of these examples, k > q. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 113–123, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10024

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The CRC Handbook of Combinatorial Designs
• D. R. Stinson
• Lamken
• Haemers