(t, m, s)-Nets and Maximized Minimum Distance

Leonhard Grünschloß (), Johannes Hanika (), Ronnie Schwede () and Alexander Keller ()
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Leonhard Grünschloß: Ulm University
Johannes Hanika: Ulm University
Ronnie Schwede: Swiss Federal Institute of Aquatic Science and Technology, Eawag
Alexander Keller: Ulm University

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 397-412 from Springer

Abstract: Summary Many experiments in computer graphics imply that the average quality of quasi-Monte Carlo integro-approximation is improved as the minimal distance of the point set grows. While the definition of (t, m, s)-nets in base b guarantees extensive stratification properties, which are best for t = 0, sampling points can still lie arbitrarily close together. We remove this degree of freedom, report results of two computer searches for (0, m, 2)-nets in base 2 with maximized minimum distance, and present an inferred construction for general m. The findings are especially useful in computer graphics and, unexpectedly, some (0, m, 2)-nets with the best minimum distance properties cannot be generated in the classical way using generator matrices.

Keywords: Minimum Distance; Computer Graphic; Generator Matrice; Latin Hypercube Sample; Elementary Interval (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_23

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DOI: 10.1007/978-3-540-74496-2_23

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