On the existence of higher order polynomial lattices based on a generalized figure of merit
Dick and Pillichshammer recently introduced generalized rank-1 polynomial lattices which can be viewed as digital (t, alpha, beta, n x m, s)-nets as introduced by the first author. In this work we generalize the figure of merit of rank-1 polynomial lattices such that the new figure of merit g, is related to the t-value, when one views the rank-1 polynomial lattice as a digital (t, alpha, beta, n x m, s)-net. Then we show the existence of rank-1 polynomial lattices for which the generalized figure of merit rho(x) satisfies a certain condition. We present some numerical results comparing the corresponding t-value to known explicit constructions. (c) 2007 Elsevier Inc. All rights reserved.
polynomial lattice figure of merit digital net