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In this paper, we formulate and investigate the following problem: given integers d,k andr where k > r 1,d 2, and a prime power q, arrange d hyperplanes on Fk q to maximize the number of r-dimensional subspaces of Fk q each of which belongs to at least one of the hyperplanes. The problem is motivated by the need to give tighter bounds for an error-tolerant pooling design based on finite vector spaces.

On a hyperplane arrangement problem and tighter analysis of an error-tolerant pooling design