{"id":"palomar/PALOMAR-2026-10-29-000041","url":"https://github.com/lgruen/quasi-uniform-sequences-lean/tree/96081a746079c3440ddf1ad0329cd5ebaeb09ab5","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000041-v1.json","repo":"https://github.com/lgruen/quasi-uniform-sequences-lean","tags":["math.NT","math.NA","msc:11K38","msc:65C05","msc:11K45","msc:52C17","msc:68V20"],"score":0,"title":"Low-discrepancy quasi-uniform digital sequences in every dimension (Halton-type failure and residue sequences)","trust":"high","domain":"math.NT","source":"palomar","authors":["Leonhard Gruenschloss"],"reviews":0,"subject":"math.NT","summary":"Two results of the manuscript \"Low-discrepancy quasi-uniform digital sequences in every dimension\" (version 1): Corollary cor:halton of Theorem thm:nonqu, and Theorem thm:residue with Corollaries cor:korobov and cor:residueQU for one explicit sequence. Quasi-uniform means here: there is a real B such that h(P_[N]) = 2, where P_[N] is the set of the first N points, h is the Euclidean covering radius of [0,1]^s (a supremum over the cube of the minimum distance to the points) and delta is the minimum Euclidean distance over pairs of distinct indices. (1) For every prime p, every s >= 2 and all…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true,"formalizes":[{"title":"Low-discrepancy quasi-uniform digital sequences in every dimension (version 1)","identifier":"doi:10.5281/zenodo.23769768","relationship":"formalizes"}]}