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

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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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     author = {N. N. Osipov},
     title = {Construction of lattice rules with a~trigonometric $d$-property on the basis of extreme lattices},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {212--219},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_2_a3/}
}
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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/