Summary. The "good lattice" theory yields a powerful method of computing approximations for the integral of functions defined on [0, 1] S through averaged sums of m evaluations. We present a continuation of the only existing table of best lattices for s = 4 up to m = 3298, and the first table for s = 5 up to m= 772. has an error bounded by KrP ~r+ 1)(g) where Kr depends only on the integrand (r is the degree of regularity), and P(r+ 1)(g) depends also on the regularity of the function and on the vector g. The class of functions considered is the class of functions of bounded variation in the sense of Hardy and Krause with certain restrictions on the periodicity of their partial derivatives which determine r. Moreover there are ways of symmetrizing an integrand such that the integral of the transformed function is equal to the original one without changing too much K r and for which r = 1. * From the "Ecole Polytechnique de Montr6al, d6partement de Math6matiques appliqu6es", C.P.6079 Station A, Montr6al QC, Canada H3C 3A7.
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