The existence of simple \(S_ 3(3,4,\nu)\)
type: Item
instance of: scholarly article
title: The existence of simple \(S_ 3(3,4,\nu)\)
zbMATH Open document ID: 0681.05009
DOI: 10.1016/0012-365X(89)90364-6
author: Scott A. Vanstone
author: Kevin T. Phelps
author: D. R. Stinson
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Here \(\nu\) is the number of elements in a set, and \(S_ 3(3,4,\nu)\) refers to a 3-design on \(\nu\) elements, each block being of size 4, and every 3-triplet of \(\nu\) elements appears exactly in 3 blocks. It is well-known that \(S_ 3(3,4,\nu)\) exists if and only if \(\nu\) is even, but the construction methods proving this result lead to configurations with repeated blocks. In this note the authors give an elementary construction technique and establish the existence of simple \(S_ 3(3,4,\nu)s\) for all even \(\nu >4\).
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4114641
zbMATH Keywords: 3-design
zbMATH Keywords: construction
MaRDI profile type: Publication
cites work: Q3686719
cites work: On Some Tactical Configurations
cites work: On resolvable designs \(S_ 3(3;4,v)\)
cites work: k-difference-cycles and the construction of cyclic t-designs
full work available at URL: 0012-365x(89)90364-6
OpenAlex ID: W2012064524
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description: scientific article; zbMATH DE number 4114641