  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 of 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.
