Whenever one uses a quasi-Monte Carlo method for cubature or optimization, it seems that there's a wide variety of low-discrepancy sequences to choose from, associated with the names of van der Corput, Halton, Hammersley, Faure, Niederreiter, Sobol', and other names I don't quite remember. Are there any good rules of thumb on how to choose the most appropriate low-discrepancy sequence for your computations?
How do I know which low-discrepancy sequence to use?
monte carlo;random
The Koksma-Hlawka Inequality states that if $f$ has bounded variation $V(f)$ in the sense of Hardy and Krause on the unit hypercube $I^s$, then the error bound is given by the product of $V(f)$ and the star-discrepancy of the sequence used. That the error depends on only the discrepancy yields two conclusions. First, choose the sequence with lowest discrepancy. Second, the regularity of the integrand plays no role in this bound and so in practice it's not very useful. To incorporate more information about the integrand into your error analysis, you have to either perform experimental comparisons between sequences or consider other approaches besides basic quasi-Monte Carlo.