Parallel Quasi-Monte Carlo Integration using (t,s)-Sequences

. Currently, the most effective constructions of low-discrepancy point sets and sequences are based on the theory of (t; m; s)-nets and (t; s)-sequences. In this work we discuss parallelization techniques for quasi-Monte Carlo integration using (t; s)-sequences. We show that leapfrog parallelization may be very dangerous whereas block-based parallelization turns out to be robust. 1 Introduction Currently, the most effective constructions of low-discrepancy point sets and sequences, which are of great importance for quasi-Monte Carlo methods in multidimensional numerical integration, are based on the concept of (t; m; s)- nets and (t; s)-sequences. A detailed theory was developed in Niederreiter [10]. High dimensional numerical integration problems may require a significant amount of computations. Therefore, substantial effort has been invested into finding techniques for performing these computations on all kinds of parallel architectures (see [8] for an exhaustive overview). In orde..