Explicit constructions in the classical mean squares problem in irregularities of point distribution

W. W L Chen*, M. M. Skriganov

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    45 Citations (Scopus)

    Abstract

    We explicitly construct distributions script D signN of N points in the n-dimensional unit cube Un with the minimal order of the L2-discrepancy ℒ2[script D signN] < Cn(log N)1/2(n-1), where the constant Cn is independent of N. The constructions are based on ideas from coding theory. In particular, we use codes over finite fields Fp with large weights simultaneously in two different metrics - the well known Hamming metric and a new non-Hamming metric arising recently in coding theory.

    Original languageEnglish
    Pages (from-to)67-95
    Number of pages29
    JournalJournal fur die Reine und Angewandte Mathematik
    Issue number545
    Publication statusPublished - 2002

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