The existence of good extensible rank-1 lattices

Please use this identifier to cite or link to this item: https://doi.org/10.1016/S0885-064X(02)00026-2

Title:	The existence of good extensible rank-1 lattices
Authors:	Hickernell, F.J. Niederreiter, H.
Keywords:	Discrepancy Extensible lattices Figures of merit Lattice rules Quasi-Monte Carlo integration
Issue Date:	Jun-2003
Citation:	Hickernell, F.J., Niederreiter, H. (2003-06). The existence of good extensible rank-1 lattices. Journal of Complexity 19 (3) : 286-300. ScholarBank@NUS Repository. https://doi.org/10.1016/S0885-064X(02)00026-2
Abstract:	Extensible integration lattices have the attractive property that the number of points in the node set may be increased while retaining the existing points. It is shown here that there exist generating vectors, h, for extensible rank-1 lattices such that for n = b, b2, ... points and dimensions s = 1, 2, ... the figures of merit Rα, Pα, and discrepancy are all small. The upper bounds obtained on these figures of merit for extensible lattices are some power of log n worse than the best upper bounds for lattices where h is allowed to vary with n and s. © 2002 Elsevier Science (USA). All rights reserved.
Source Title:	Journal of Complexity
URI:	http://scholarbank.nus.edu.sg/handle/10635/104291
ISSN:	0885064X
DOI:	10.1016/S0885-064X(02)00026-2
Appears in Collections:	Staff Publications

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