### 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.

Original language | English |
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Pages (from-to) | 59-78 |

Number of pages | 20 |

Journal | Journal of Geometry |

Volume | 98 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Aug 1 2010 |

### Keywords

- Blocking sets
- Linearity conjecture

### ASJC Scopus subject areas

- Geometry and Topology

## Fingerprint Dive into the research topics of 'Small point sets of PG(n, p <sup>3h</sup>) intersecting each line in 1 mod p<sup>h</sup>points'. Together they form a unique fingerprint.

## Cite this

Harrach, N. V., Metsch, K., Szonyi, T., & Weiner, Z. (2010). Small point sets of PG(n, p

^{3h}) intersecting each line in 1 mod p^{h}points.*Journal of Geometry*,*98*(1-2), 59-78. https://doi.org/10.1007/s00022-010-0051-1