Article
The B-Adic Diaphony of Digital Sequences
Authors
Abstract
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 Z b, s = 1, . . . , b. This formula shows that for a fixed s ∈ {1, . . . , b}, the b-adic diaphony has the same values for any digital (0, s)-sequence over Z b. For t > 0 we show upper bounds on the b- adic diaphony of digital (t, s)-sequences over Z b. We also consider the asymptotic behavior of the b-adic diaphony of these digital sequences.
Keywords
Digital (t, s)-sequence, b-adic diaphony, Walsh function, generator matrices.
Citation
Greslehner, J. (2010). The b-adic diaphony of digital sequences. Uniform Distribution Theory, 5(2), 87–112.
J. Greslehner, “The b-adic diaphony of digital sequences,” Uniform Distribution Theory, vol. 5, no. 2, pp. 87–112, 2010.
Greslehner J. The b-adic diaphony of digital sequences. Uniform Distribution Theory. 2010;5(2):87–112.
Greslehner, J. (2010), ‘The b-adic diaphony of digital sequences’, Uniform Distribution Theory, 5(2), pp. 87–112.
Greslehner, Julia. “The B-adic Diaphony of Digital Sequences.” Uniform Distribution Theory, vol. 5, no. 2, 2010, pp. 87–112.
Greslehner, Julia. “The B-adic Diaphony of Digital Sequences.” Uniform Distribution Theory 5, no. 2 (2010): 87–112.
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Published by: Engineering Journals
