A note on sub-orthogonal lattices

TL;DR

This paper demonstrates that for any k-dimensional lattice, there exists a sequence of lattices with sub-orthogonal lattices converging to it, and discusses conditions for faster convergence.

Contribution

It introduces a method to approximate any lattice with a sequence of lattices having sub-orthogonal lattices, enhancing understanding of lattice convergence and structure.

Findings

Existence of lattice sequences converging to any given lattice

Conditions identified for faster convergence of lattice sequences

Extension of lattice approximation techniques

Abstract

It is shown that, given any $k$-dimensional lattice $\Lambda$, there is a lattice sequence $\Lambda_w$, $w\in \mathbb Z$, with sub-orthogonal lattice $\Lambda_o \subset \Lambda$, converging to $\Lambda$ (unless equivalence), also we discuss the conditions for faster convergence.