Randomly Permuted (t,m,s)-Nets and (t, s)-Sequences

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Abstract

This article presents a hybrid of Monte Carlo and Quasi-Monte Carlo methods. In this hybrid, certain low discrepancy point sets and sequences due to Faure, Niederreiter and Sobol’ are obtained and their digits are randomly permuted. Since this randomization preserves the equidistribution properties of the points it also preserves the proven bounds on their quadrature errors. The accuracy of an estimated integrand can be assessed by replication, consisting of independent re-randomizations.