Partial covers of PG(n,q)
Combinatorics
2012-10-04 v1
Abstract
In this paper, we show that a set of q+a hyperplanes, q>13, a<(q-10)/4, that does not cover PG(n,q), does not cover at least q^(n-1)-aq^(n-2) points, and show that this lower bound is sharp. If the number of non- covered points is at most q^(n-1), then we show that all non-covered points are contained in one hyperplane. Finally, using a recent result of Blokhuis, Brouwer, and Szonyi [3], we remark that the bound on a for which these results are valid can be improved to a<(q-2)/3 and that this upper bound on a is sharp
Cite
@article{arxiv.1210.1002,
title = {Partial covers of PG(n,q)},
author = {Stefan Dodunekov and Leo Storme and Geertrui Van de Voorde},
journal= {arXiv preprint arXiv:1210.1002},
year = {2012}
}