Recently, a notion of $(t; e; s)$-sequences in base $b$ was introduced, where $e =(e_1 ,..., e_s)$ is a positive integer vector, and their discrepancy bounds were obtainedbased on the signed splitting method. In this paper, we rst propose a generalframework of $ ({\bf{T}}_{\mathcal{E}},{\mathcal{E}}, s)$-sequences, and present that it includes $ (\bf{T}, s)$-sequencesand $ (t; e; s)$-sequences as special cases. Next, we show that a careful analysis leadsto 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 boundis given by$$c^∗_s =\frac{b^{t}} {s!} \Pi\limits^s_ i=1 \frac{ b^{e_{i}} − 1} {2e_i log b}.$$
@article{301,
title = {Improvement on the discrepancy of (t, e, s)-sequences},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v59i0.301},
language = {EN},
url = {http://dml.mathdoc.fr/item/301}
}
Tezuka, Shu. Improvement on the discrepancy of (t, e, s)-sequences. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v59i0.301. http://gdmltest.u-ga.fr/item/301/