## Probabilistic constructions in generalized quadrangles

- Jeroen Schillewaert, Jacques Verstraëte
- Discrete Mathematics
- 2015

- Published 2004

Lower bounds for the size of a complete partial ovoid in a nondegenerate Hermitian surface are obtained. For even characteristic, a sharp bound is obtained and all examples of this size are described. Next, a general construction method for locally hermitian partial ovoids is explained, which leads to interesting small examples. Finally, a conjecture is given for the size of the largest complete strictly partial ovoid. By using partial derivation, several examples of complete strictly partial ovoids of this size are provided.

@inproceedings{Aguglia2004OnPO,
title={On partial ovoids of Hermitian surfaces},
author={Angela Aguglia and Gary L. Ebert and Deirdre Luyckx},
year={2004}
}