A Tool for Custom Construction of QMC and RQMC Point Sets

TL;DR

LatNet Builder is a software tool designed to optimize parameters for lattice and digital net constructions in QMC and RQMC methods, improving integration accuracy in high-dimensional spaces.

Contribution

The paper introduces LatNet Builder, a new software tool that facilitates the construction of efficient QMC and RQMC point sets with customizable figures of merit.

Findings

Supports various Hilbert spaces and discrepancy measures

Provides effective search algorithms for point set construction

Demonstrates practical applications with simple illustrations

Abstract

We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the $s$-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets of coordinates. They are upper bounds on the worst-case error (for QMC) or variance (for RQMC) for integrands rescaled to have a norm of at most one in certain Hilbert spaces of functions. We summarize what are the various Hilbert spaces, discrepancies, types of weights, figures of merit, types of constructions, and search methods supported by LatNet Builder. We briefly discuss its organization and we provide simple illustrations of what it can do.