<abstract xmlns="http://www.w3.org/1999/xhtml">Recently, a notion of (t, e, s)-sequences in base b was introduced, where e = (e1, . . . , es) is a positive integer vector, and their discrepancy bounds were obtained based on the signed splitting method. In this paper, we first propose a general framework of (Tε , ε, s)-sequences, and present that it includes (T, s)-sequences and (t, e, s)-sequences as special cases. Next, we show that a careful analysis leads to an asymptotic improvement on the discrepancy bound of a (t, e, s)-sequence in an even base b. It follows that the constant in the leading term of the star discrepancy bound is given by<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-3.jpg"></inline-graphic></alternatives></inline-formula></abstract>

Recently, a notion of (t, e, s)-sequences in base b was introduced, where e = (e1, . . . , es) is a positive integer vector, and their discrepancy bounds were obtained based on the signed splitting method. In this paper, we first propose a general framework of (Tε , ε, s)-sequences, and present that it includes (T, s)-sequences and (t, e, s)-sequences as special cases. Next, we show that a careful analysis leads to an asymptotic improvement on the discrepancy bound of a (t, e, s)-sequence in an even base b. It follows that the constant in the leading term of the star discrepancy bound is given by

Improvement on the Discrepancy of (t, e, s)-Sequences

Institute of Mathematics for Industry Kyushu University 744 Motooka, Nishi-ku, Fukuoka-shi Fukuoka-ken 819–0395 JAPAN

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Improvement on the Discrepancy of (t, e, s)-Sequences"}

Recently, a notion of (t, e, s)-sequences in base b was introduced, where e = (e1, . . . , es) is a positive integer vector, and their discrepancy bounds were...

Improvement on the Discrepancy of (t, e, s)-Sequences

Published Online: Mar 11, 2015

Page range: 27 - 38

Received: Jun 26, 2014

DOI: https://doi.org/10.2478/tmmp-2014-0016

Keywords
low-discrepancy sequences, signed splitting method, (t, e, s)-sequences

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Improvement on the Discrepancy of (t, e, s)-Sequences

Published Online: Mar 11, 2015

Page range: 27 - 38

Received: Jun 26, 2014

DOI: https://doi.org/10.2478/tmmp-2014-0016

Keywordslow-discrepancy sequences, signed splitting method, (t, e, s)-sequences

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
low-discrepancy sequences, signed splitting method, (t, e, s)-sequences