Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation

Authors:
Pierre L'Ecuyer
Affiliations:
DIRO, CIRRELT, and GERAD, Université de Montréal, Canada
Venue:
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Year:
2008

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Abstract

Algorithmic random number generators require recurring sequences with very long periods and good multivariate uniformity properties. Point sets and sequences for quasi-Monte Carlo numerical integration need similar multivariate uniformity properties as well. It then comes as no surprise that both types of applications share common (or similar) construction methods. However, there are some differences in both the measures of uniformity and the construction methods used in practice. We briefly survey these methods and explain some of the reasons for the differences.