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Small point sets of PG(n, p 3h) intersecting each line in 1 mod p h points

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Abstract

The main result of this paper is that point sets of PG(n, q), q = p 3h, p ≥ 7 prime, of size < 3(q n-1 + 1)/2 intersecting each line in 1 modulo \({\sqrt[3] q}\) points (these are always small minimal blocking sets with respect to lines) are linear blocking sets. As a consequence, we get that minimal blocking sets of PG(n, p 3), p ≥ 7 prime, of size < 3(p 3(n-1) + 1)/2 with respect to lines are always linear.

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Authors and Affiliations

  1. Department of Computer Science, Eötvös Loránd University, Pázmány Péter stny. 1/C, 1117, Budapest, Hungary

    Nóra V. Harrach & Tamás Szőnyi

  2. Matematisches Intitut, Justus-Liebig-Universität Gießen, Arndtstrasse 2, 35392, Gießen, Germany

    Klaus Metsch

  3. Computer and Automation Research Institute of the Hungarian Academy of Sciences, Lágymányosi út 11, 1111, Budapest, Hungary

    Tamás Szőnyi & Zsuzsa Weiner

  4. Prezi, Krúdy Gyula utca 12, 1088, Budapest, Hungary

    Zsuzsa Weiner

Authors
  1. Nóra V. Harrach
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  2. Klaus Metsch
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  3. Tamás Szőnyi
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  4. Zsuzsa Weiner
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Correspondence to Zsuzsa Weiner.

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Harrach, N.V., Metsch, K., Szőnyi, T. et al. Small point sets of PG(n, p 3h) intersecting each line in 1 mod p h points. J. Geom. 98, 59–78 (2010). https://doi.org/10.1007/s00022-010-0051-1

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  • DOI: https://doi.org/10.1007/s00022-010-0051-1

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