<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We introduce a hybridization of digital sequences with uniformly distributed sequences in the domain of <italic>b</italic>-adic integers, ℤ<italic>b,b</italic> ∈ℕ \ {1}, by using such sequences as input for generating matrices. The generating matrices are then naturally required to have finite row-lengths. We exhibit some relations of the ‘classical’ digital method to our extended version, and also give several examples of new constructions with their respective quality assessments in terms of <italic>t</italic>, <bold>T</bold> and discrepancy.</p></abstract>

We introduce a hybridization of digital sequences with uniformly distributed sequences in the domain of b-adic integers, ℤb,b ∈ℕ \ {1}, by using such sequences as input for generating matrices. The generating matrices are then naturally required to have finite row-lengths. We exhibit some relations of the ‘classical’ digital method to our extended version, and also give several examples of new constructions with their respective quality assessments in terms of t, T and discrepancy.

An Extension of the Digital Method Based on <italic>b</italic>-Adic Integers

Institute of Financial Mathematics and Applied Number Theory

Uniform distribution theory

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An Extension of the Digital Method Based on -Adic Integers

We introduce a hybridization of digital sequences with uniformly distributed sequences in the domain of b-adic integers, ℤb,b ∈ℕ \ {1}, by using such sequences...

An Extension of the Digital Method Based on b-Adic Integers

Published Online: Jul 20, 2018

Page range: 87 - 107

Received: Jun 19, 2017

Accepted: Nov 21, 2017

DOI: https://doi.org/10.1515/udt-2018-0005

Keywords
quasi-Monte Carlo methods, construction, digital method, digit expansion, -adic integers

© 2018 Roswitha Hofer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

An Extension of the Digital Method Based on b-Adic Integers

Published Online: Jul 20, 2018

Page range: 87 - 107

Received: Jun 19, 2017

Accepted: Nov 21, 2017

DOI: https://doi.org/10.1515/udt-2018-0005

Keywordsquasi-Monte Carlo methods, construction, digital method, digit expansion, -adic integers

© 2018 Roswitha Hofer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
quasi-Monte Carlo methods, construction, digital method, digit expansion, -adic integers