Dagstuhl Seminar on Algorithms and Complexity for Continuous Problems location location:Schloss Dagstuhl, Wadern, Germany date:20-25 September 2009
The concept of K-optimal lattices was introduced by Cools and Lyness (2001) to set up searches for lattice rules for multivariate integration with a low number of points for a given trigonometric degree of precision. The original searches were restricted to 3 and 4 dimensions. Refinements were later made to make the searches possible in 5 and 6 dimensions. The idea behind K-optimal lattices was extended in Russia using extremal lattices.
In this talk these approaches to lattice rule construction will be described
and a survey of the obtained results will be presented.