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.
|Number of pages||29|
|Journal||Journal fur die Reine und Angewandte Mathematik|
|Publication status||Published - 2002|