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 [8], 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.
['Stefan M. Dodunekov', 'Leo Storme', 'G. Van de Voorde']
Partial covers of PG(n,q)