Quasi-Monte Carlo methods for integration of functions with dominating mixed smoothness in arbitrary dimension

In a celebrated construction, Chen and Skriganov gave explicit examples of point sets achieving the best possible L2L2-norm of the discrepancy function. We consider the discrepancy function of the Chen–Skriganov point sets in Besov spaces with dominating mixed smoothness and show that they also achieve the best possible rate in this setting. The proof uses a bb-adic generalization of the Haar system and corresponding characterizations of the Besov space norm. Results for further function spaces and integration errors are concluded.