A method for constructing quasimultiple affine planes of arbitrary order
type: Item
instance of: scholarly article
title: A method for constructing quasimultiple affine planes of arbitrary order
zbMATH Open document ID: 0821.05002
author: Michael Wertheimer
author: J. F. Dillon
author: Glenn F. Stahly
published in: Finite Fields and their Applications
publication date: 1995-07-05T00:00:00Z
review text: The authors consider the problem of constructing quasimultiple designs of an affine plane of an arbitrary order \(n\) (even if no such plane exists), i.e. the existence problem for \((n^ 2, n, n\lambda)\)-designs. In this context, it is of interest to determine the smallest such \(\lambda\), a problem considered by the reviewer in his paper [``On the existence of small quasimultiples of affine and projective planes of arbitrary order'', Discrete Math. 85, No. 2, 177-189 (1990; Zbl 0729.05009)]. The present authors give a construction using 2-transitive groups which allows them to obtain several improvements on the previously known bounds; in particular, a quasidouble (i.e. \(\lambda= 2\)) is obtained for \(n= 28\).
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 759429
zbMATH Keywords: quasimultiple designs
zbMATH Keywords: affine plane
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
full work available at URL: ffta.1995.1018
OpenAlex ID: W1971483333
DOI: 10.1006/FFTA.1995.1018
description: scientific article; zbMATH DE number 759429