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

@article{Ngo2008OnAH,
  title={On a hyperplane arrangement problem and tighter analysis of an error-tolerant pooling design},
  author={Hung Q. Ngo},
  journal={J. Comb. Optim.},
  year={2008},
  volume={15},
  pages={61-76}
}
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, arranged hyperplanes onFq to maximize the number of r-dimensional subspaces of Fq 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. 

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