CUBATURE RULES OF PRESCRIBED MERIT

We introduce a criterion for the evaluation of multidimensional quadra ture, or cubature, rules for the hypercube: this is the merit of a rul e which is closely related to its trigonometric degree and which reduc es to the Zaremba figure of merit in the case of a lattice rule. We de rive a family of rules Q(k)(s) having dimension s and merit 2(k). Thes e rules seem to be competitive with lattice rules with respect to the merit that can be achieved with a given number of abscissas.