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There is no Drake/Larson linear space on 30 points

✍ Scribed by Anton Betten; Dieter Betten

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 173 KB
Volume: 18
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20231

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✦ Synopsis

Abstract

A linear space is Drake/Larson if it contains at least two lines and there are no lines of size 2, 3 or 6. The existence or nonexistence of such linear spaces on v points is known except for v=30. The purpose of this article is to settle the remaining case on thirty points in the negative. This result relies on a combination of parameter calculation and exhaustive computer search. © 2009 Wiley Periodicals, Inc. J Combin Designs 28: 48–70, 2010

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## Abstract Let __L__ denote the set of positive integers that do not divide 6. In 1983, Drake and Larson determined all positive integers __v__ such that there is a proper PBD(__v__,__L__) with one exception, namely, the integer __v__ = 30. (Recall that a PBD is __proper__ if there is no block tha