On hybrid point sets stemming from Halton-type Hammersley point sets and polynomial lattice point sets

TL;DR

This paper introduces a new class of hybrid point sets combining Halton-type Hammersley and polynomial lattice point sets, demonstrating their low discrepancy properties for quasi-Monte Carlo methods.

Contribution

It extends the concept of hybrid point sets by incorporating polynomial lattice components over finite fields, providing existence results for low discrepancy sets.

Findings

Existence of low discrepancy hybrid point sets with polynomial lattice components

Extension of hybrid point set theory to finite fields and polynomial rings

Potential applications in quasi-Monte Carlo integration

Abstract

In this paper we consider finite hybrid point sets that are the digital analogs to finite hybrid point sets introduced by Kritzer. Kritzer considered hybrid point sets that are a combination of lattice point sets and Hammersley point sets constructed using the ring of integers and the field of rational numbers. In this paper we consider finite hybrid point sets whose components stem from Halton-type Hammersley Point sets and lattice point sets which are constructed using the arithmetic of the ring of polynomials and the field of rational functions over a finite field. We present existence results for such finite hybrid point sets with low discrepancy.