Constructing \(t\)-designs from \(t\)-wise balanced designs
type: Item
instance of: scholarly article
title: Constructing \(t\)-designs from \(t\)-wise balanced designs
zbMATH Open document ID: 1161.05010
author: J. P. McSorley
author: Leonard H. Soicher
published in: European Journal of Combinatorics
publication date: 2007-02-14T00:00:00Z
review text: Let \(X\) be a finite set of nonzero cardinality \(v\) and \(B\) be a nonempty collection of subsets of \(X\). If each subset of \(X\) with cardinality \(t>0\) is contained in exactly \(\lambda>0\) of the elements of \(B\), then this structure is called a \(t\)-wise balanced design. This paper provides a procedure for constructing from such a design, a balanced design (called a \(t\)-design) with all the elements of \(B\) having the same cardinality. It is shown that the automorphism group of the new design contains as a subgroup, the automorphism group of the original design. The construction is also used to produce a \(t\)-design for a smaller set (\(X\) with one point removed). The authors state that their construction was found as a result of looking for 2-designs with repeated blocks to help fill up the catalogue by \textit{D. A. Preece} [A selection of BIBDs with repeated blocks, \(r \leq 20\), \(\text{gcd}(b,r,\lambda)=1\), 2003 (Preprint)]. They also provide examples constructed and tested with the DESIGN package in GAP (http://www.gap-system.org, 2004).
reviewed by: V. S. Ramamurthi
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 5126363
zbMATH Keywords: balanced design
zbMATH Keywords: BIBD
describes a project that uses: GAP
describes a project that uses: DESIGN
MaRDI profile type: Publication
full work available at URL: j.ejc.2005.02.003
OpenAlex ID: W2015564254
cites work: Q4873725
cites work: Q4040932
DOI: 10.1016/J.EJC.2005.02.003
description: scientific article; zbMATH DE number 5126363