Low-discrepancy quasi-uniform digital sequences in every dimension
A sequence of points in the unit cube is quasi-uniform if its first $N$ points are spread like a grid for every $N$: no two of them are closer, and no empty ball between them is larger, than a constant times $N^{-1/s}$ in dimension $s$. Dick, Goda and Suzuki asked for such sequences among the digital sequences of quasi-Monte Carlo integration, and Goda, Hofer and Suzuki asked whether any Halton-type sequence is quasi-uniform. We show that in dimension two and higher no Halton-type sequence, no Sobol' sequence, no classical Niederreiter sequence and no Faure sequence is quasi-uniform, and…
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