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

Hiroki Kajiura; Makoto Matsumoto; Kosuke Suzuki

doi:10.1016/j.ffa.2018.04.011

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arXiv · 1801.02152

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

Hiroki Kajiura·Makoto Matsumoto·Kosuke Suzuki

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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 $B^3=I$.

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Hiroki Kajiura, Makoto Matsumoto, Kosuke Suzuki. 2018-01-07. Characterization of matrices $B$ such that $(I,B,B^2)$ generates a digital net with $t$-value zero. https://doi.org/10.1016/j.ffa.2018.04.011

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