Robust numerical integration and pairwise independent random variables

A numerical integration method by means of random samples is called robust, if the variance of its error is as small as that of the i.i.d.-sampling for any integrand. To reduce the randomness of robust numerical integration, we use pairwise random samples instead of i.i.d. samples. Among others, we recommend the discrete random Weyl sampling for the quick generation of pairwise independent samples.