{"id":"hexagon/2610.00664","pdf":"https://hexagonmath.org/pdf/2610.00664v1","url":"https://hexagonmath.org/abs/2610.00664v1","tags":["math.MG","math.NT","msc:11K38","msc:65C05","msc:11K45","msc:52C17","msc:68V20","Halton sequences","Lean 4 formalization","covering radius"],"score":0,"title":"Low-discrepancy quasi-uniform digital sequences in every dimension","domain":"math.NA","origin":"ai-generated","source":"hexagon","authors":["Leonhard Gruenschloss"],"reviews":0,"subject":"math.NA","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-29-000041&version=1"],"human_understanding":"some"}