Several 2-(46,6,3) designs
type: Item
instance of: scholarly article
title: Several 2-(46,6,3) designs
zbMATH Open document ID: 0723.05013
DOI: 10.1016/0012-365X(91)90075-D
published in: Discrete Mathematics
publication date: 1991-01-01T00:00:00Z
review text: A t-(v,k,\(\lambda\)) design is a set of v points with a collection of k- subsets called blocks, so that any t points lie in exactly \(\lambda\) blocks. For \(t=2\) the design is the ordinary balanced incomplete block design (BIBD). Using the usual extension approach this paper provides a construction method for 2-(46,6,3) designs based on the unique generalized quadrangle H of order (4,2). This quadrangle can be realized as the totally singular points and lines of a Hermitian variety in PG(3,4). Apart from H itself two other structures are used, namely, a 5- edge colouring of \(K_ 5\) and a punctured projective plane of order 2. The construction results in a large class of non-isomorphic 2-(46,6,3) designs, which is a new result because only such design was known before. The author also presents designs for two related parameter sets. An interesting large class of non-isomorphic 2-(298,10,5) designs is given with the author's query that does not know of any previous construction of such a design.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 62K10
zbMATH DE Number: 4191643
zbMATH Keywords: t-(v,k,\(\lambda \) ) design
zbMATH Keywords: balanced incomplete block design (BIBD)
zbMATH Keywords: generalized quadrangle
zbMATH Keywords: 5-edge colouring of \(K_ 5\)
zbMATH Keywords: punctured projective plane of order 2.
author: Peter J. Cameron
reviewed by: B. Leo Raktoe
MaRDI profile type: Publication
cites work: Q3686719
cites work: Q5184922
cites work: Q3701436
cites work: Q3344217
description: scientific article; zbMATH DE number 4191643