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We introduce a criterion for the evaluation of multidimensional quadrature, or cubature, rules for the hypercube: this is the merit of a rule, which is closely related to its trigonometric degree, and which reduces to the Zaremba figure of merit in the case of a lattice rule. We derive a family of rules Q; having dimension s and merit 2'. These rules seem to be competitive with lattice rules with respect to the merit that can be achieved with a given number of abscissas.doi:10.2172/211665 fatcat:2ry23jxrwfhihjfajf65l3uaqi