Implementation and tests of low-discrepancy sequences

Abstract

Low-discrepancy sequences are used for numerical integration, in simulation, and in related applications. Techniques for producing such sequences have been proposed by, among others, Halton, Sobol´, Faure, and Niederreiter. Niederreiter's sequences have the best theoretical asymptotic properties. The paper describes two ways to implement the latter sequences on a computer and discusses the results obtained in various practical tests on particular integrals.