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

Currently, in the context of quasi-Monte Carlo applications the most effect ive low-discrepancy sequences are digital (t, s)-sequences. Recently, we have demonstrated [11] that leaping parallelization of (t, s)- sequences as suggested by Bromley [3] may lead to dramatic defects in numer ical integration whereas block based parallelization behaves very stable. T hese results have been achieved experimentally for leaps and block sizes wh ich are a power of 2. We present generalizations, possible explanations for the effects observed, and possible solutions to these problems. Additionally, we present discrep ancy estimates for leaped and blocked subsequences of digital (t, s)-sequen ces. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved .