Abstract
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 $$ 0.80822 \ldots \cdot \Delta ^4 (1 + o(1)), \Delta \to \infty $$ (d = 2Δ − 1 ≥ 3 is an arbitrary odd number). With few exceptions, the resulting lattice rules have the highest previously known effectiveness factor.
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