The lifting construction: A general solution for the fat strut problem

Abstract

A cylinder anchored at two distinct points of the lattice ℤn is called a strut if its interior does not contain a lattice point. We address the problem of constructing struts of maximal radius in ℤn. Our main result is a general construction technique, which we call the lifting construction, which produces a sequence of struts that are optimal in the limit. We also tighten a previous result of ours—an achievable lower bound on the volume of a strut. The problem is motivated by a nonlinear analog communication problem. We demonstrate, through simulation, improvements in performance that are obtained using our construction.