Kronecker-Halton sequences in $\mathbb{F}_p((X^{-1}))$

TL;DR

This paper studies the distribution and discrepancy of hybrid sequences combining Halton and digital Kronecker sequences over polynomial rings, providing criteria for uniform distribution.

Contribution

It introduces a full criterion for uniform distribution of these hybrid sequences and analyzes their discrepancy properties.

Findings

Criteria for uniform distribution established

Discrepancy bounds derived for hybrid sequences

Enhanced understanding of sequence distribution in polynomial rings

Abstract

In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and prove results on the discrepancy of such hybrid sequences.