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An upper bound on the minimal dispersion

2017; Elsevier BV; Volume: 45; Linguagem: Inglês

10.1016/j.jco.2017.11.003

ISSN

1090-2708

Autores

Mario Ullrich, Jan Vybíral,

Tópico(s)

Digital Image Processing Techniques

Resumo

For ε∈(0,1∕2) and a natural number d≥2, let N be a natural number with N≥29log2(d)log2(1∕ε)ε2.We prove that there is a set of N points in the unit cube [0,1]d, which intersects all axis-parallel boxes with volume ε. That is, the dispersion of this point set is bounded from above by ε.

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