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

  • Leonhard Grünschloß
  • Johannes Hanika
  • Ronnie Schwede
  • Alexander Keller
Conference paper


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.


Minimum Distance Computer Graphic Generator Matrice Latin Hypercube Sample Elementary Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Leonhard Grünschloß
    • 1
  • Johannes Hanika
    • 1
  • Ronnie Schwede
    • 2
  • Alexander Keller
    • 1
  1. 1.Ulm UniversityGermany
  2. 2.EawagSwiss Federal Institute of Aquatic Science and TechnologySwitzerland

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