  We consider the local discrepancy of a symmetrized version of Hammersley type
point sets in the unit square. As a measure for the irregularity of
distribution we study the norm of the local discrepancy in Besov spaces with
dominating mixed smoothness. It is known that for Hammersley type points this
norm has the best possible rate provided that the smoothness parameter of the
Besov space is nonnegative. While these point sets fail to achieve the same for
negative smoothness, we will prove in this note that the symmetrized versions
overcome this defect. We conclude with some consequences on discrepancy in
further function spaces with dominating mixed smoothness and on numerical
integration based on quasi-Monte Carlo rules.
