On the L p discrepancy of two-dimensional folded Hammersley point sets

We give an explicit construction of two-dimensional point sets whose L _p discrepancy is of best possible order for all \({1 \le p \le \infty}\) . It is provided by folding Hammersley point sets in base b by means of the b-adic baker’s transformation which has been introduced by Hickernell (Monte Carlo and quasi-Monte Carlo methods. Springer, Berlin, 274–289, 2002) for b =  2 and Goda, Suzuki, and Yoshiki (The b-adic baker’s transformation for quasi-Monte Carlo integration using digital nets. arXiv:1312.5850 math:NA], 2013) for arbitrary \({b \in \mathbb{N}}\) , \({b \ge 2}\) . We prove that both the minimum Niederreiter–Rosenbloom–Tsfasman weight and the minimum Dick weight of folded Hammersley point sets are large enough to achieve the best possible order of L _p discrepancy for all \({1 \le p \le \infty}\) .