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Some results on the existence of large sets of t-designs

✍ Scribed by G. B. Khosrovshahi; R. Tayfeh-Rezaie

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 96 KB
Volume: 11
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.10027

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✦ Synopsis

Abstract

A set of trivial necessary conditions for the existence of a large set of t‐designs, LSN, is $N\big | {{\nu \hskip -3.1 \nu}-i \choose k-i}$ for i = 0,…,t. There are two conjectures due to Hartman and Khosrovshahi which state that the trivial necessary conditions are sufficient in the cases N = 2 and 3, respectively. Ajoodani‐Namini has established the truth of Hartman's conjecture for t = 2. Apart from this celebrated result, we know the correctness of the conjectures for a few small values of k, when N = 2 and t ≤ 6, and also when N = 3 and t ≤ 4. In this article, we show that similar results can be obtained for infinitely many values of k. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 144–151, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10027

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