Innovations in Incidence Geometry

Small maximal partial ovoids of $H(3,q^2)$

Klaus Metsch

Abstract

The trivial lower bound for the size of a maximal partial ovoid of $H ( 3 , q 2 )$ is $q 2 + 1$. Ebert showed that this bound can be attained if and only if $q$ is even. In the present paper it is shown that a maximal partial ovoid of $H ( 3 , q 2 )$, $q$ odd, has at least $q 2 + 1 + 4 9 q$ points (previously, only $q 2 + 3$ was known). It is also shown that a maximal partial spread of $H ( 3 , q 2 )$, $q$ even, has size $q 2 + 1$ or size at least $q 2 + 1 + 4 9 q$.

Article information

Source
Innov. Incidence Geom., Volume 3, Number 1 (2006), 1-12.

Dates
Received: 14 March 2006
Accepted: 8 May 2006
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323233

Digital Object Identifier
doi:10.2140/iig.2006.3.1

Mathematical Reviews number (MathSciNet)
MR2267602

Zentralblatt MATH identifier
1108.51015

Citation

Metsch, Klaus. Small maximal partial ovoids of $H(3,q^2)$. Innov. Incidence Geom. 3 (2006), no. 1, 1--12. doi:10.2140/iig.2006.3.1. https://projecteuclid.org/euclid.iig/1551323233

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