کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4608634 | 1338368 | 2014 | 14 صفحه PDF | دانلود رایگان |

The term low-discrepancy sequences is widely used to refer to ss-dimensional sequences XX for which the bound D∗(N,X)≤cs(logN)s+O((logN)s−1)D∗(N,X)≤cs(logN)s+O((logN)s−1) is satisfied, where D∗D∗ denotes the usual star discrepancy. In this paper, we study such bounds for (t,s)(t,s)-sequences and a newer class of low-discrepancy sequences called (t,e,s)-sequences, introduced recently by Tezuka (2013). In the first case, by using a combinatorial argument coupled with a careful worst-case analysis, we are able to improve the discrepancy bounds from Faure and Lemieux (2012) for (t,s)(t,s)-sequences. In the second case, an adaptation of the same pair of arguments allows us to improve the asymptotic behavior of the bounds from Tezuka (2013) in the case of even bases.
Journal: Journal of Complexity - Volume 30, Issue 5, October 2014, Pages 620–633