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

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

Author

Listed:
  • Leonhard Grünschloß

    (Ulm University)

  • Johannes Hanika

    (Ulm University)

  • Ronnie Schwede

    (Swiss Federal Institute of Aquatic Science and Technology, Eawag)

  • Alexander Keller

    (Ulm University)

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.

Suggested Citation

  • Leonhard Grünschloß & Johannes Hanika & Ronnie Schwede & Alexander Keller, 2008. "(t, m, s)-Nets and Maximized Minimum Distance," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 397-412, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_23
    DOI: 10.1007/978-3-540-74496-2_23
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