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

@article{Cools2001ThreeAF,
  title={Three- and four-dimensional K-optimal lattice rules of moderate trigonometric degree},
  author={Ronald Cools and James N. Lyness},
  journal={Math. Comput.},
  year={2001},
  volume={70},
  pages={1549-1567}
}
A systematic search for optimal lattice rules of specified trigonometric degree d over the hypercube [0, 1)s has been undertaken. The search is restricted to a population K(s, δ) of lattice rules Q(Λ). This includes those where the dual lattice Λ⊥ may be generated by s points h for each of which |h| = δ = 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 s = 3, d ≤ 29 and s = 4, d ≤ 23… CONTINUE READING
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