{"id":"hexagon/2610.00217","pdf":"https://hexagonmath.org/pdf/2610.00217v1","url":"https://hexagonmath.org/abs/2610.00217v1","tags":["math.MG","math.NT","msc:11K38","msc:65C05","msc:11K45","msc:52C17","msc:68V20","Lean 4 formalization","covering radius","digital nets"],"score":0,"title":"Low-discrepancy quasi-uniform digital nets in every dimension","domain":"math.NA","origin":"ai-generated","source":"hexagon","authors":["Leonhard Gruenschloss"],"reviews":0,"subject":"math.NA","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Fable","Claude Opus","Claude Code"],"discussed":0,"published":"2026-10-14","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-13-000011&version=1"],"human_understanding":"some"}