Characterization of matrices $B$ such that $(I,B,B^2)$ generates a digital net with $t$-value zero

Abstract

We study $3$-dimensional digital nets over ${\mathbb{F}}_2$ generated by matrices $(I,B,B^2)$ where $I$ is the identity matrix and $B$ is a square matrix. We give a characterization of $B$ for which the $t$-value of the digital net is $0$. As a corollary, we prove that such $B$ satisfies $B^3=I$.

References in corpus (1)

• Consistency of Markov chain quasi-Monte Carlo on continuous state spaces

Cited by in corpus (4)

• Analysis and Synthesis of Digital Dyadic Sequences
• A table of short-period Tausworthe generators for Markov chain quasi-Monte Carlo
• Characterization of digital $(0,m,3)$-nets and digital $(0,2)$-sequences in base $2$
• A search for short-period Tausworthe generators over ${\mathbb{F}}_b$ with application to Markov chain quasi-Monte Carlo