Constructions of lattices via biquadratic and triquadratic fields
Number Theory
2025-09-08 v1
Abstract
The lattices and are known to be the densest lattices in dimensions 4 and 8, respectively. In this paper, we employ tools from algebraic number theory to prove that the -lattice arises from an infinite family of totally imaginary biquadratic fields. Furthermore, we extend this construction to show that both the and can be realized via triquadratic fields derived from this family.
Keywords
Cite
@article{arxiv.2509.04591,
title = {Constructions of lattices via biquadratic and triquadratic fields},
author = {L. F. Santos and G. C. Jorge},
journal= {arXiv preprint arXiv:2509.04591},
year = {2025}
}