Generating and Testing the Modified Halton Sequences
The Halton sequences are one of the most popular low-sdiscrepancy sequences, used for calculating multi-dimensional integrals or in quasi-Monte Carlo simulations. Various techniques for their randomization exist. One of the authors proved that for one such modification an estimate of the discrepancy with a very small constant before the leading term can be proved. In this paper we describe an efficient algorithm for generating these sequences on computers and show timing results, demonstrating the efficiency of the algorithm. We also compare the integration error of these sequences with that of the classical Halton sequences on families of functions widely used for such benchmarking purposes. The results demonstrate that the modified Halton sequences can be used successfully in quasi-Monte Carlo methods.
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