Transversal designs of block size eight and nine
type: Item
instance of: scholarly article
title: Transversal designs of block size eight and nine
zbMATH Open document ID: 0840.05013
author: Charles J. Colbourn
published in: European Journal of Combinatorics
publication date: 1996-07-04T00:00:00Z
review text: The author uses a mixture of direct and recursive constructions to almost settle the existence problem for transversal designs with index \(\lambda> 1\) and block sizes \(k= 8\) and \(k= 9\) (with just a few open cases). This is a major result, since it is the first result that goes beyong the work of Hanani who settled the corresponding problem for \(k= 7\), see \textit{H. Hanani} [On transversal designs. Combinatorics, Part 1, Proc. Advanced Study Inst., Breukelen, 42-52 (1974; Zbl 0312.05016)]. The author's proof uses some (generalization of) standard methods, e.g. quasi-difference matrices and \(V(m, t)\) vectors for direct constructions and Wilson-type theorems for recursive constructions, and a new concept (the so-called ``outline transversal design'') which turns out to be a very powerful tool which should have further applications.
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 847626
zbMATH Keywords: transversal designs
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
full work available at URL: eujc.1996.0001
OpenAlex ID: W2031498817
DOI: 10.1006/EUJC.1996.0001
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description: scientific article; zbMATH DE number 847626