Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Good low degree rank-1 lattice rules of high dimension

Author: Tor Sørevik
Journal: Math. Comp. 85 (2016), 1821-1835
MSC (2010): Primary 65D32; Secondary 42A10
Published electronically: January 7, 2016
MathSciNet review: 3471109
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we introduce a novel approach to searching for rank-1 lattice rules. The idea is to separate the search into two steps, first finding good generating vectors and then finding the corresponding optimal $ N$ value. For the trigonometric degree $ \delta = 5$ we establish a simple criterion on the generating vectors. By using the theory for Golomb rulers and $ {\mathcal B}_2$-series we construct efficient algorithms for finding good generating vectors. Combined with our own home-brewed algorithm for finding the corresponding optimal $ N$, we produce new good rank-1 lattice rules of high dimension.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65D32, 42A10

Retrieve articles in all journals with MSC (2010): 65D32, 42A10

Additional Information

Tor Sørevik
Affiliation: Department of Mathematics, University of Bergen, Bergen, Norway

Keywords: Optimal lattice rules, trigonometric degree, Golomb rulers
Received by editor(s): February 27, 2014
Received by editor(s) in revised form: October 29, 2014, and January 7, 2015
Published electronically: January 7, 2016
Dedicated: In memory of James N. Lyness
Article copyright: © Copyright 2016 American Mathematical Society