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The $b$-adic diaphony of digital sequences

Author(s): Julia Greslehner

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 5;
Issue: 2;
Start page: 87;
Date: 2010;
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Keywords: Digital (t | s)-sequence | b-adic diaphony | Walsh function | generator matrices

The $b$-adic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this article we give a formula for the $b$-adic diaphony of digital $(0, s)$-sequences over $\mathbb{Z}_b$, $s=1, \ldots, b$. This formula shows that for a fixed $s \in {1, \ldots, b}$,the $b$-adic diaphony has the same values for any digital $(0, s)$-sequence over $\mathbb{Z}_b$. For $t > 0$ we show upper bounds on the $b$-adic diaphony of digital $(t, s)$-sequences over $\mathbb{Z}_b$. We also consider the asymptotic behavior of the $b$-adic diaphony of these digital sequences.
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