Asymptotically optimal unsaturated lattice cubature formulae with bounded boundary layer

This paper describes a new algorithm for constructing lattice cubature formulae with bounded boundary layer. These formulae are unsaturated (in the sense of Babenko) both with respect to the order and in regard to the property of asymptotic optimality on W2m-spaces, m element of (n/2,∞). Most of the results obtained apply also to W2μ(Rn)-spaces with a hypoelliptic multiplier of smoothness μ. Bibliography: 6 titles