On sequences of projections of the cubic lattice

Details On sequences of projections of the cubic lattice On sequences of projections of the cubic lattice

2011-10-13

arxiv.org/abs/1110.2995v1

Mathematics

Combinatorics

16 pages, 5 figures

Scientific paper

In this paper we study sequences of lattices which are, up to similarity, projections of $\mathbb{Z}^{n+1}$ onto a hyperplane $\bm{v}^{\perp}$ for $\bm{v} \in \mathbb{Z}^{n+1}$ 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.

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