{"id":"palomar/PALOMAR-2026-10-13-000011","url":"https://github.com/lgruen/separated-nets-lean/tree/d7b5f50530f21871c58c462a049385c1e1c1b1fa","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-13-000011-v1.json","repo":"https://github.com/lgruen/separated-nets-lean","tags":["math.NT","math.NA","msc:11K38","msc:65C05","msc:11K45","msc:52C17","msc:68V20","quasi-monte-carlo","digital-nets","number-theory"],"score":0,"title":"Low-discrepancy quasi-uniform digital nets in every dimension","trust":"high","domain":"math.NT","source":"palomar","authors":["Leonhard Gruenschloss"],"reviews":0,"subject":"math.NT","summary":"The main theorem (thm:A, Theorem A \"Every dimension\", of version 1) of the manuscript \"Low-discrepancy quasi-uniform digital nets in every dimension\", in one statement. For every dimension s >= 3, every integer base q >= 2 all of whose prime factors are at least s - 1, and every k >= 1, the explicit digital net P^{U*_s}_{k,q} over Z/qZ with N = q^(sk) points (Definition def:Ns for the places infinity, 0, 1, ..., s-2 -- the Faure-Hammersley frame in graph form with the gauges of prop:Ns and prop:Gs -- and the design U*_s of Definition def:Ustar, whose columns are short vectors of the lattices…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-13","reactions":{},"formalized":true,"formalizes":[{"title":"Low-discrepancy quasi-uniform digital nets in every dimension (version 1)","identifier":"doi:10.5281/zenodo.23327749","relationship":"formalizes"}]}