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arXiv · 2512.15007

Hidden low-discrepancy structures in random point sets

Kohei Suzuki·Takashi Goda
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Abstract

We study the probabilistic existence of point configurations satisfying the $(0, m, d)$-net property in base $b$ within a randomly generated point set of size $N$ in the $d$-dimensional unit cube. We first derive an upper bound on the number of geometric patterns for $(0, m, d)$-nets in base $b$. By applying the elementary probability bounds together with this counting result, we then give scaling conditions on $N$ as a function of $m$ such that this probability converges to $1$ and $0$, respectively.

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Kohei Suzuki, Takashi Goda. 2026-02-18. Hidden low-discrepancy structures in random point sets. https://arxiv.org/abs/2512.15007

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