Fat struts: Constructions and a bound

Given a lattice A C R, a cylinder anchored at two lattice points is called a strut if its interior does not contain a lattice point. We wish to determine the maximum radius of a strut of given length. Optimal struts are constructed in Z3 and Z4. We also derive, using a nonconstructive but elementary argument, an achievable lower bound on the product Z∊, where I and ∊ are the length and radius of a strut in Zn. The motivation for the problem comes from studying nonlinear analog communication systems.

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