An algorithm to compute the $t$-value of a digital net and of its projections

Abstract: Digital nets are among the most successful methods to construct low-discrepancy point sets for quasi-Monte Carlo integration. Their quality is traditionally assessed by a measure called the $t$-value. A refinement computes the $t$-value of the projections over subsets of coordinates and takes a weighted average (or some other function) of these values. It is also of interest to compute the $t$-values of embedded nets obtained by taking subsets of the points. In this paper, we propose an efficient algorithm to compute such measures and we compare our approach with previously proposed methods both empirically and in terms of computational complexity.