Quasi-Monte Carlo Integration : Results from the Practice

Several test functions, whose variation could be calculated, were integrated with up tp 10 trials using different low-discrepancy sequences in dimensions 3, 6, 12, and 24. The errors divided by the variation were compared with exact and asymptotic discrepancies. The errors follow an approximate power law, whose constant is essentially given by the variance of the integrand, and whose power depends on its effective dimension. Included were also some calculations with scrambled Niederreiter sequences. A notable result is that the pre-factors in the asymptotic discrepancy function D*(N), which are so often used as a quality measure of the sequences, have little relevance in practical ranges of N