Asymptotic properties of locally extensible designs
type: Item
instance of: scholarly article
title: Asymptotic properties of locally extensible designs
zbMATH Open document ID: 0532.05008
DOI: 10.1007/BF00147650
published in: Geometriae Dedicata
publication date: 1984-01-01T00:00:00Z
review text: From the authors' abstract: ``An \((n+1,1)\)-design \(D\) is locally extensible at a block \(B\) if \(D\) can be embedded in an \((n+1,1)\)-design having a block \(B^*\) of cardinality \(n+1\) and such that \(B\subset B^*\). If \(D\) is embeddable in a finite projective plane of order \(n\), then \(D\) is called globally extensible. In this paper, we investigate the asymptotic behaviour of locally extensible designs and Euclidean designs. We study the relationship between locally extensible and extensible designs and the uniqueness of such embeddings. It is shown that, for \(n, l\) and \(t\) sufficiently large, any \((n+1,1)\)-design which has minimum block length \(l\) and which is locally extensible at \(t\) of its blocks is globally extensible.''
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 3843757
zbMATH Keywords: extending designs
zbMATH Keywords: projective plane
zbMATH Keywords: globally extensible
zbMATH Keywords: Euclidean designs
author: Ronald C. Mullin
author: Scott A. Vanstone
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3843757