Numerische Mathematik

, Volume 99, Issue 2, pp 349–363 | Cite as

A new class of equal-weight integration rules on the hypercube

  • Neil A. ButlerEmail author


This paper introduces a new class of equal-weight integration rules on the hypercube. The points are cyclically generated in a different way to the method of good lattice points. The main justification for these integration rules is that they are capable of having high degree under a slight modification to the definition of degree. Some theorems are presented which provide conditions under which congruential integration rules exist for degree up to thirteen. Actual integration rules are provided for up to seven million points and up to five hundred dimensions.


Mathematical Method Slight Modification Lattice Point Actual Integration Integration Rule 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamUK

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