Construction algorithms for plane nets in base $b$

TL;DR

This paper introduces two algorithms for constructing plane (0,m,2)-nets in base b, which are important for uniform point distribution in numerical integration.

Contribution

It presents novel algorithms specifically designed for constructing plane (0,m,2)-nets in base b, enhancing their practical generation.

Findings

Algorithms successfully construct plane (0,m,2)-nets

Improved methods for generating low-discrepancy point sets

Potential for better quasi-Monte Carlo integration

Abstract

The class of $(0,m,s)$-nets in base $b$ has been introduced by Niederreiter as examples of point sets in the $s$-dimensional unit cube with excellent uniform distribution properties. In particular such nets have been proved to have very low discrepancy. This property is essential for the use of nets in quasi-Monte Carlo rules for numerical integration. In this short note we propose two algorithms for the construction of plane $(0,m,2)$-nets in base~$b$.