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On sequences of projections of the cubic lattice (1110.2995v2)
Published 13 Oct 2011 in math.CO, cs.CG, cs.IT, and math.IT
Abstract: In this paper we study sequences of lattices which are, up to similarity, projections of $\mathbb{Z}{n+1}$ onto a hyperplane $\bm{v}{\perp}$, with $\bm{v} \in \mathbb{Z}{n+1}$ and converge to a target lattice $\Lambda$ which is equivalent to an integer lattice. We show a sufficient condition to construct sequences converging at rate $O(1/ |\bm{v}|{2/n})$ and exhibit explicit constructions for some important families of lattices.