Thwarts in transversal designs
type: Item
instance of: scholarly article
title: Thwarts in transversal designs
zbMATH Open document ID: 0822.05007
DOI: 10.1007/BF01388383
author: Charles J. Colbourn
author: J. H. Dinitz
author: Mieczysław Wojtas
published in: Designs, Codes and Cryptography
publication date: 1995-05-04T00:00:00Z
review text: A subset of points in a transversal design is a thwart if each block in the design has one of a small number of intersection sizes with the subset. While the details are too complicated to state here, the authors study thwarts (subconfigurations) of transversal deisgns via the use of a version of Wilson's theorem. As a consequence they are able to obtain improved bounds for \(N(n)\), the maximum number of mutually orthogonal latin squares of order \(n\), for 25 values of \(n\leq 8096\). The connection between transversal designs and sets of orthogonal latin squares comes from the well-known result: \(N(n)\geq k\) if and only if there exists a transversal design \(\text{TD}(k+ 2; n)\).
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 751327
zbMATH Keywords: transversal design
zbMATH Keywords: thwart
zbMATH Keywords: Wilson's theorem
zbMATH Keywords: mutually orthogonal latin squares
reviewed by: Gary L. Mullen
MaRDI profile type: Publication
cites work: Q4190650
cites work: More mutually orthogonal latin squares
cites work: On seven mutually orthogonal latin squares
cites work: Concerning the number of mutually orthogonal latin squares
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description: scientific article; zbMATH DE number 751327