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

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Abstract

In this paper, we formulate and investigate the following problem: given integers d,k and r where k>r≥1,d≥2, and a prime power q, arrange d hyperplanes on \(\mathbb{F}_{q}^{k}\) to maximize the number of r-dimensional subspaces of \(\mathbb{F}_{q}^{k}\) 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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Authors and Affiliations

  1. Computer Science and Engineering Department, SUNY at Buffalo, Amherst, NY, 14260, USA

    Hung Q. Ngo

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  1. Hung Q. Ngo
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Correspondence to Hung Q. Ngo.

Additional information

This work is partially supported by NSF CAREER Award CCF-0347565.

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Ngo, H.Q. On a hyperplane arrangement problem and tighter analysis of an error-tolerant pooling design. J Comb Optim 15, 61–76 (2008). https://doi.org/10.1007/s10878-007-9084-2

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  • DOI: https://doi.org/10.1007/s10878-007-9084-2

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