On the Lp discrepancy of two-dimensional folded Hammersley point sets

We give an explicit construction of two-dimensional point sets whose Lp discrepancy is of best possible order for all 1≤p≤∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1 \le p \le \infty}$$\end{document}. 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∈N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${b \in \mathbb{N}}$$\end{document}, b≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${b \ge 2}$$\end{document}. 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 Lp discrepancy for all 1≤p≤∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1 \le p \le \infty}$$\end{document}.