On difference matrices, transversal designs, resolvable transversal designs and large sets of mutually orthogonal F-squares
type: Item
instance of: scholarly article
title: On difference matrices, transversal designs, resolvable transversal designs and large sets of mutually orthogonal F-squares
zbMATH Open document ID: 0659.05034
DOI: 10.1016/0378-3758(87)90060-7
published in: Journal of Statistical Planning and Inference
publication date: 1987-01-01T00:00:00Z
review text: For p a prime power and for many values of \(\lambda\), (mixed) difference matrices \(D(k,\lambda;EA(p),Z_ p)\) with \(k=\lambda\) or \(\sim \lambda\) are constructed. These matrices are then used to construct resolvable TD(r,\(\lambda\) ;p) (transversal designs with \(\lambda\) p blocks on r point classes of size p) with \(r=\lambda\) or \(\sim \lambda\). Many of these designs are G-regular. We then use these resolvable TD's to construct many nearly half complete (non-resolvable) TD(r,\(\lambda\) ;p), nearly quarter complete sets of mutually orthogonal F-squares F(\(\lambda\),\(\lambda\) /p), and nearly half complete difference matrices D(k,\(\lambda\) ;EA(p)). In addition, recently constructed generalized Hadamard matrices are used to construct many complete or nearly complete examples of the above combinatorial systems. For example, for all odd prime powers \(p>5\) we show there is a \(TD(r,4p^{m+1};p)\), \(m\geq 0\), with r falling short of the Bose-Bush bound by 1.
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 05B99
Mathematics Subject Classification ID: 51D99
zbMATH DE Number: 4077240
zbMATH Keywords: resolvable transversal designs
zbMATH Keywords: G-regular transversal designs
zbMATH Keywords: nets
zbMATH Keywords: balanced generalized weighing matrices
zbMATH Keywords: generalized Bhaskar Rao designs
zbMATH Keywords: difference matrices
zbMATH Keywords: F-squares
zbMATH Keywords: generalized Hadamard matrices
zbMATH Keywords: combinatorial systems
author: Warwick de Launey
MaRDI profile type: Publication
full work available at URL: 0378-3758(87)90060-7
OpenAlex ID: W2001102524
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description: scientific article; zbMATH DE number 4077240