Digital Nets and Sequences for Quasi-Monte Carlo Methods

TL;DR

This paper introduces new methods for digital nets and sequences to enhance quasi-Monte Carlo techniques, including randomization, discrepancy analysis, and evolutionary optimization, with practical applications demonstrated.

Contribution

It presents three novel results: randomized digital nets, discrepancy distribution of scrambled nets, and improved digital nets via evolutionary computation.

Findings

Randomized digital nets implementation

Discrepancy distribution of scrambled nets analyzed

Enhanced digital nets through evolutionary algorithms

Abstract

Quasi-Monte Carlo methods are a way of improving the efficiency of Monte Carlo methods. Digital nets and sequences are one of the low discrepancy point sets used in quasi-Monte Carlo methods. This thesis presents the three new results pertaining to digital nets and sequences: implementing randomized digital nets, finding the distribution of the discrepancy of scrambled digital nets, and obtaining better quality of digital nets through evolutionary computation. Finally, applications of scrambled and non-scrambled digital nets are provided.