### Abstract

Let m′_{2}(3, q) be the largest value of k(k2+1) for which there exists a complete k-cap in PG(3, q), q even. In this paper, the known upper bound on m′_{2}(3, q) is improved. We also describe a number of intervals, for k, for which there does not exist a complete k-cap in PG(3, q), q even. These results are then used to improve the known upper bounds on the number of points of a cap in PG(n, q), q even, n≥4.

Original language | English |
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Pages (from-to) | 163-169 |

Number of pages | 7 |

Journal | Geometriae Dedicata |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1993 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Geometriae Dedicata*,

*45*(2), 163-169. https://doi.org/10.1007/BF01264518

**Caps in PG(n, q), q even, n≥3.** / Storme, L.; Szőnyi, T.

Research output: Contribution to journal › Article

*Geometriae Dedicata*, vol. 45, no. 2, pp. 163-169. https://doi.org/10.1007/BF01264518

}

TY - JOUR

T1 - Caps in PG(n, q), q even, n≥3

AU - Storme, L.

AU - Szőnyi, T.

PY - 1993/2

Y1 - 1993/2

N2 - Let m′2(3, q) be the largest value of k(k2+1) for which there exists a complete k-cap in PG(3, q), q even. In this paper, the known upper bound on m′2(3, q) is improved. We also describe a number of intervals, for k, for which there does not exist a complete k-cap in PG(3, q), q even. These results are then used to improve the known upper bounds on the number of points of a cap in PG(n, q), q even, n≥4.

AB - Let m′2(3, q) be the largest value of k(k2+1) for which there exists a complete k-cap in PG(3, q), q even. In this paper, the known upper bound on m′2(3, q) is improved. We also describe a number of intervals, for k, for which there does not exist a complete k-cap in PG(3, q), q even. These results are then used to improve the known upper bounds on the number of points of a cap in PG(n, q), q even, n≥4.

UR - http://www.scopus.com/inward/record.url?scp=0013548635&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013548635&partnerID=8YFLogxK

U2 - 10.1007/BF01264518

DO - 10.1007/BF01264518

M3 - Article

VL - 45

SP - 163

EP - 169

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 2

ER -