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Abstract: Extensible (polynomial) lattice point sets have the property that the number N of points in the node set of a quasi-Monte Carlo algorithm may be increased while retaining the existing points. Explicit constructions for extensible (polynomial) lattice point sets have been presented recently by Niederreiter and Pillichshammer. It is the aim of this paper to establish extensibility for a powerful generalization of polynomial lattice point sets, the so-called hyperplane nets. [Copyright &y& Elsevier]

Abstract: In this paper we consider two problems, finding minimal polynomials over and over of a finite-length sequence over , in a lattice and its sublattice respectively using lattice theory over polynomial rings. And we deduce a relationship between them by a lattice basis transformation matrix. As a byproduct, we present a new synthesis algorithm for the first problem just using operations in instead of as in Berlekamp–Massey algorithm. [Copyright &y& Elsevier]