Mathematics of computation vol:70 issue:236 pages:1549-1567
A systematic search for optimal lattice rules of specified trigonometric degree d over the hypercube (0, 1)(s) has been undertaken. The search is restricted to a population K(s, delta) of lattice rules Q(A). This includes those where the dual lattice Lambda (perpendicular to) may be generated by s points h for each of which h = delta = d + 1. The underlying theory, which suggests that such a restriction might be helpful, is presented. The general character of the search is described, and, for s = 3, d less than or equal to 29 and s = 4, d less than or equal to 23, a list of K-optimal rules is given. It is not known whether these are also optimal rules in the general sense; this matter is discussed.