### 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 |
---|---|

Pages (from-to) | 59-78 |

Number of pages | 20 |

Journal | Journal of Geometry |

Volume | 98 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Aug 2010 |

### Fingerprint

### Keywords

- Blocking sets
- Linearity conjecture

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

^{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

**Small point sets of PG(n, p ^{3h}) intersecting each line in 1 mod p^{h}points.** / Harrach, Nóra V.; Metsch, Klaus; Szőnyi, T.; Weiner, Zsuzsa.

Research output: Contribution to journal › Article

^{3h}) intersecting each line in 1 mod p

^{h}points',

*Journal of Geometry*, vol. 98, no. 1-2, pp. 59-78. https://doi.org/10.1007/s00022-010-0051-1

^{3h}) intersecting each line in 1 mod p

^{h}points. Journal of Geometry. 2010 Aug;98(1-2):59-78. https://doi.org/10.1007/s00022-010-0051-1

}

TY - JOUR

T1 - Small point sets of PG(n, p 3h) intersecting each line in 1 mod phpoints

AU - Harrach, Nóra V.

AU - Metsch, Klaus

AU - Szőnyi, T.

AU - Weiner, Zsuzsa

PY - 2010/8

Y1 - 2010/8

N2 - The main result of this paper is that point sets of PG(n, q), q = p3h, p ≥ 7 prime, of size ≥ 3(qn-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, p3), p ≥ 7 prime, of size ≥ 3(p3(n-1) + 1)/2 with respect to lines are always linear.

AB - The main result of this paper is that point sets of PG(n, q), q = p3h, p ≥ 7 prime, of size ≥ 3(qn-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, p3), p ≥ 7 prime, of size ≥ 3(p3(n-1) + 1)/2 with respect to lines are always linear.

KW - Blocking sets

KW - Linearity conjecture

UR - http://www.scopus.com/inward/record.url?scp=79953249917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953249917&partnerID=8YFLogxK

U2 - 10.1007/s00022-010-0051-1

DO - 10.1007/s00022-010-0051-1

M3 - Article

AN - SCOPUS:79953249917

VL - 98

SP - 59

EP - 78

JO - Journal of Geometry

JF - Journal of Geometry

SN - 0047-2468

IS - 1-2

ER -