Small proper double blocking sets in Galois planes of prime order
type: Item
instance of: scholarly article
title: Small proper double blocking sets in Galois planes of prime order
zbMATH Open document ID: 1149.51001
author: Petr Lisoněk
author: Joanna Wallis
published in: Discrete Mathematics
publication date: 2008-09-04T00:00:00Z
review text: A double blocking set on \(\text{PG}(2,q)\) is a set \(B\) of points that intersects every line in at least two points. A double blocking set \(B\) is called proper if \(| B\cap\ell| \leq p-1\) for every line \(\ell\), i.e. the complement of \(B\) is again a double blocking set. The smallest known example of a proper blocking set in \(\text{PG}(2,p)\), \(p\) prime, was the disjoint union of two triangles of size \(3(p+1)/2\), i.e. a blocking set of size \(3(p+1)\). In this note, the authors construct proper blocking sets in \(\text{PG}(2,p)\) of size \(3p+1\) for each prime \(p\equiv3\pmod{4}\) and of size \(3p+2\) for each prime \(p\geq7\).
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51A30
zbMATH DE Number: 5321277
zbMATH Keywords: blocking set
zbMATH Keywords: double blocking set
zbMATH Keywords: Galois plane
reviewed by: I. Landjev
MaRDI profile type: Publication
full work available at URL: j.disc.2007.07.103
OpenAlex ID: W2000564617
cites work: Q4354373
cites work: On the size of a blocking set in \(\text{PG}(2,p)\)
cites work: Construction of \((n, r)\)-arcs in \(PG(2, q)\)
cites work: Q4370894
DOI: 10.1016/J.DISC.2007.07.103
description: scientific article; zbMATH DE number 5321277