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Low-discrepancy quasi-uniform digital nets in every dimension

Leonhard Gruenschloss

Palomar Registrypalomar/PALOMAR-2026-10-13-000011Oct 13, 2026math.NTscore 0

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…

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