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

W. W L Chen; M. M. Skriganov

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 journal › Article › peer-review

59 Citations (Scopus)

Abstract

We explicitly construct distributions script D sign_N of N points in the n-dimensional unit cube Uⁿ with the minimal order of the L₂-discrepancy ℒ₂[script D sign_N] < C_n(log N)^1/2(n-1), where the constant C_n is independent of N. The constructions are based on ideas from coding theory. In particular, we use codes over finite fields F_p 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 language	English
Pages (from-to)	67-95
Number of pages	29
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	545
Publication status	Published - 2002

Cite this

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title = "Explicit constructions in the classical mean squares problem in irregularities of point distribution",

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.",

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AB - 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.

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

Abstract

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