Abstract. We show that a specific even unimodular lattice of dimension 80, first investigated by Schulze-Pillot and others, is extremal (i.e., the minimal nonzero norm is 8). Thi...
Abstract. We discuss periodization of smooth functions f of d variables for approximation of multivariate integrals. The benefit of periodization is that we may use lattice rules,...
In this paper we introduce construction algorithms for Korobov rules for numerical integration which work well for a given set of dimensions simultaneously. The existence of such ...
Josef Dick, Friedrich Pillichshammer, Benjamin J. ...
I show how to design the value of the diffusion constant D for the random walks of Squares and Triangles over their respective regular lattice in two-dimensions. By allowing moveme...