Improvement on the discrepancy of (t,e,s)-sequences

Rok, strany: 2014, 27 - 38

Recently, a notion of $(t,{\bf e},s)$-sequences in base $b$ was introduced, where ${\bf e}=(e_1,\ldots,e_s)$ 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 $(\T_{{\mathcal E}}, {\mathcal E},s)$-sequences, and present that it includes $(\T,s)$-sequences and $(t,{\bf e},s)$-sequences as special cases. Next, we show that a careful analysis leads to an asymptotic improvement on the discrepancy bound of a $(t,{\bf e},s)$-sequence in an even base $b$. It follows that the constant in the leading term of the star discrepancy bound is given by

ISO 690:

Tezuka, S. 2014. Improvement on the discrepancy of (t,e,s)-sequences. In Tatra Mountains Mathematical Publications, vol. 59, no.2, pp. 27-38. 1210-3195.

APA:

Tezuka, S. (2014). Improvement on the discrepancy of (t,e,s)-sequences. Tatra Mountains Mathematical Publications, 59(2), 27-38. 1210-3195.