Digital nets in dimension two with the optimal order of L_p discrepancy

Abstract

We study the L p discrepancy of two-dimensional digital nets for finite p. In the year 2001 Larcher and Pillichshammer identified a class of digital nets for which the symmetrized version in the sense of Davenport has L 2 discrepancy of the order logN/N, which is best possible due to the celebrated result of Roth. However, it remained open whether this discrepancy bound also holds for the original digital nets without any modification.