Techniques for parallel quasi-Monte Carlo integration with digital sequences and associated problems Original Research Article

Currently, in the context of quasi-Monte Carlo applications the most effective low-discrepancy sequences are digital (t, s)-sequences. Recently, we have demonstrated that leaping parallelization of (t, s)-sequences as suggested by Bromley may lead to dramatic defects in numerical integration whereas block based parallelization behaves very stable. These results have been achieved experimentally for leaps and block sizes which are a power of 2. We present generalizations, possible explanations for the effects observed, and possible solutions to these problems. Additionally, we present discrepancy estimates for leaped and blocked subsequences of digital (t, s)-sequences.