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.
Categories: math.CO cs.CG cs.IT math.IT