Discrepancy Between Qmc and Rqmc, Ii

There are two types of randomization for (t, m, d)-nets: Owen scrambling and random digital shift. In the previous paper [Uniform Distribution Theory, 2 (2007), 93-105], we introduced a class of functions for which any Sobol’ points have zero integration error, whereas Owen scrambling of Sobol’ points has the same variance of integration error as that of simple Monte Carlo methods. In this paper, by using the same functions as the paper mentioned above, we con- struct an example of functions for which any Sobol’ points have zero integration error, whereas not only Owen scrambling but also random digital shift of Sobol’ points have variance of integration error no smaller than that of simple Monte Carlo methods.