Partial covers of

Abstract: In this paper, we show that a set of hyperplanes, , , that does not cover , does not cover at least points, and show that this lower bound is sharp. If the number of non-covered points is at most , then we show that all non-covered points are contained in one hyperplane. Finally, using a recent result of Blokhuis, Brouwer and Szőnyi , we remark that the bound on for which these results are valid can be improved to and that this upper bound on is sharp. [Copyright &y& Elsevier]