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

Hung Q. Ngo ()
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Hung Q. Ngo: SUNY at Buffalo

Journal of Combinatorial Optimization, 2008, vol. 15, issue 1, No 5, 76 pages

Abstract: 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.

Keywords: Hyperplane arrangement; Non-adaptive pooling design; Group testing; Error-tolerant (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10878-007-9084-2

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