Hans Becker, Frank Schmidt, et al.
Photomask and Next-Generation Lithography Mask Technology 2004
It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods [5]. In this paper, a new class of low-discrepancy sequences Nβ is constructed by using the ergodic theoretical transformation which is called β-adic transformation [7,8]. Here, β is a real number greater than 1. When β is an integer greater than 2, Nβ becomes the classical van der Corput sequence in base β. Therefore, the class Nβ can be regarded as a generalization of the van der Corput sequence. It is shown that for some special β, the discrepancy of this sequence decreases in the fastest order O(N 1logN). We give the numerical results of discrepancy of Nβ for some βs. Pagès [6] also generalized van der Corput sequence in a different direction by using an ergodic transformation. © 1998 IMACS/Elsevier Science B.V.
Hans Becker, Frank Schmidt, et al.
Photomask and Next-Generation Lithography Mask Technology 2004
Arnon Amir, Michael Lindenbaum
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nimrod Megiddo
Journal of Symbolic Computation
Peter Wendt
Electronic Imaging: Advanced Devices and Systems 1990