Uniform point sets and the collision test

Ahmet Göncü*, Giray Ökten

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Monte Carlo and quasi-Monte Carlo methods are popular numerical tools used in many applications. The quality of the pseudorandom sequence used in a Monte Carlo simulation is essential to the accuracy of its estimates. Likewise, the quality of the low-discrepancy sequence determines the accuracy of a quasi-Monte Carlo simulation. There is a vast literature on statistical tests that help us assess the quality of a pseudorandom sequence. However, for low-discrepancy sequences, assessing quality by estimating discrepancy is a very challenging problem, leaving us with no practical options in very high dimensions. In this paper, we will discuss how a certain interpretation of the well-known collision test for pseudorandom sequences can be used to obtain useful information about the quality of low-discrepancy sequences. Numerical examples will be used to illustrate the applications of the collision test.

Original languageEnglish
Pages (from-to)798-804
Number of pages7
JournalJournal of Computational and Applied Mathematics
Issue numberPART B
Publication statusPublished - 2014


  • Collision test
  • Error bounds
  • Quasi-Monte Carlo
  • Uniform point sets

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