On the $L_p$ discrepancy of two-dimensional folded Hammersley point sets

Abstract

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 (2002) for $b=2$ and Goda, Suzuki and Yoshiki (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 $1\le p\le \infty$.

References in corpus (1)

• The $b$-adic tent transformation for quasi-Monte Carlo integration using digital nets

Cited by in corpus (3)

• Digital nets with infinite digit expansions and construction of folded digital nets for quasi-Monte Carlo integration
• Optimal order of $L_p$-discrepancy of digit shifted Hammersley point sets in dimension 2
• The $b$-adic symmetrization of digital nets for quasi-Monte Carlo integration