Discrepancy of Generalized Hammersley Type Point Sets in Besov Spaces With Dominating Mixed Smoothness

The symmetrized Hammersley point set is known to achieve the best possible rate for the L 2-norm of the discrepancy function. Also lower bounds for the norm in Besov spaces with dominating mixed smoothness are known. In this paper a large class of point sets which are generalizations of the Hammersley type point sets are proved to asymptotically achieve the known lower bound of the Besov norm. The proof uses a b-adic generalization of the Haar system. This result can be regarded as a preparation for the proof in arbitrary dimension.