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A lower bound on the number of Semi-Boolean quadruple systems

✍ Scribed by Marco Buratti; Alberto Del Fra

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
135 KB
Volume
11
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

A Steiner quadruple system of order 2^n^ is Semi‐Boolean (SBQS(2^n^) in short) if all its derived triple systems are isomorphic to the point‐line design associated with the projective geometry PG(nβˆ’1, 2). We prove by means of explicit constructions that for any n, up to isomorphism, there exist at least 2^⌊ 3(nβˆ’4)/2βŒ‹^ regular and resolvable SBQS(2^n^). Β© 2003 Wiley Periodicals, Inc. J Combin Designs 11: 229–239, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10050

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