Geodesic
Construction of lattice rules with a trigonometric $d$-property on the basis of extreme lattices
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 2, pp. 212-219 
N. N. Osipov. Construction of lattice rules with a trigonometric $d$-property on the basis of extreme lattices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 2, pp. 212-219. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Lattice rules with the trigonometric $d$-property that are optimal with respect to the number of points are constructed for the approximation of integrals over an $n$-dimensional unit cube. An extreme lattice for a hyperoctahedron at $n=4$ is used to construct lattice rules with the trigonometric $d$-property and the number of points $$ 0.80822\ldots\cdot\Delta^4(1+o(1)),\quad\Delta\to\infty $$ ($d=2\Delta-1\ge3$ is an arbitrary odd number). With few exceptions, the resulting lattice rules have the highest previously known effectiveness factor.

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