Implementation of irreducible Sobol sequences in prime power bases

TL;DR

This paper explores various implementations of irreducible Sobol sequences, comparing their efficiency and quality, and introduces methods that improve their practical application in quasi-random sequence generation.

Contribution

The paper introduces new implementation strategies for irreducible Sobol sequences, leveraging their connection to Niederreiter sequences and equidistribution criteria.

Findings

The proposed implementations show promising numerical results.

Using Niederreiter sequence connection simplifies implementation.

Parameter search based on equidistribution improves sequence quality.

Abstract

We present different implementations for the irreducible Sobol (IS) sequences introduced in [3]. For this purpose we retain two strategies: first we use the connection between IS and Niederreiter sequences to provide a very simple implementation requiring no computer search; then we use criteria measuring the equidistribution to search for good parameters. Numerical results comparing these IS sequences to known implementations show promise for the proposed approaches.