Three- and four-dimensional <IMG >-optimal lattice rules of moderate trigonometric degree期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Three- and four-dimensional -optimal lattice rules of moderate trigonometric degree

Authors:	Ronald Cools James N Lyness

Institution:	Department of Computer Science, K. U. Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium ; Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439 and School of Mathematics, University of New South Wales, Sydney 2052 Australia

Abstract:	A systematic search for optimal lattice rules of specified trigonometric degree over the hypercube has been undertaken. The search is restricted to a population $K(s,\delta)$ of lattice rules $Q(\Lambda )$ . This includes those where the dual lattice $\Lambda ^\perp$ may be generated by points $\bf h$ for each of which $\vert{\bf h} \vert = \delta =d+1$ . The underlying theory, which suggests that such a restriction might be helpful, is presented. The general character of the search is described, and, for , $d \leq 29$ and , $d \leq 23$ , a list of -optimal rules is given. It is not known whether these are also optimal rules in the general sense; this matter is discussed.

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