Low-discrepancy quasi-uniform digital nets in every dimension
Dick, Goda and Suzuki asked for low-discrepancy digital nets that are quasi-uniform, with minimum distance $\delta$ and covering radius both of the optimal order $N^{-1/s}$, and stated the problem as open in dimension $s\ge3$. We construct such nets in every dimension. For every $s\ge3$, every base $q$ whose prime factors are at least $s-1$, and every $k\ge1$, we give explicit digital $(0,sk,s)$-nets over $\Z/q\Z$ with $N=q^{sk}$ points, covering radius at most $\sqrt s\,N^{-1/s}$, and $\delta N^{1/s}\ge1-a^*_s/q$ once $q\ge5a^*_s+4$. The constant $a^*_s\le e^{s\log s+O(s)}$ is computed from…
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