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On c-Bhaskar Rao designs with block size 4

✍ Scribed by Malcolm Greig; Spencer P. Hurd; Judson S. McCranie; Dinesh G. Sarvate

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 203 KB
Volume: 10
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.10009

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✦ Synopsis

Abstract

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ~min~=−λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ − 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ−c ≠ 2 for c > 0 and whenever c − λ~min~≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10009

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