Small complete caps in \(PG(r,q)\), \(r\geq 3\)
type: Item
instance of: scholarly article
title: Small complete caps in \(PG(r,q)\), \(r\geq 3\)
zbMATH Open document ID: 0892.51009
DOI: 10.1016/S0012-365X(96)00324-X
author: Giorgio Faina
author: Fernanda Pambianco
published in: Discrete Mathematics
publication date: 1998-02-17T00:00:00Z
review text: A \(k\)-cap in \(PG(r,q)\), is a set of \(k\) points such that no three of them are collinear and, a \(k\)-cap is complete if it is maximal with respect to set-theoretic inclusion. Determining the largest and the smallest size of a complete cap of \(PG(r,q)\) seems to be a very hard problem. The authors, after surveying the known results on the minimal size of a complete cap of \(PG(r,q)\), give some new examples of complete caps in \(PG(3,q)\) and \(PG(4,q)\), which are, for particular values of \(q\), smaller than the caps so far constructed.
Mathematics Subject Classification ID: 51E22
zbMATH DE Number: 1110063
zbMATH Keywords: caps
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1110063