Optimal Polynomials for (T,M,S)-Nets and Numerical Integration of Multivariate Walsh Series

Abstract

Existence theorems for good parameters in a construction of low-discrepancy point sets based on rational functions over finite fields are proved. A special class of these point sets is introduced and good parameters in the construction of these special point sets are tabulated. In this way, point sets in the s-dimensional unit cube for $3 \leq s \leq 15$ are obtained with very small discrepancy. These special point sets yield excellent numerical results when applied to the quasi-Monte Carlo integration of multivariate Walsh series.