Constructions of lattices via biquadratic and triquadratic fields

2025/09/04 by Luísa Santos, Santos, L. F., Guilherme Jorge +1
Computer Science · Engineering · #11H06 #11H31 #11R11 #11R16 #Advanced Numerical Analysis Techniques #Digital Image Processing Techniques #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2509.04591

openalex publication_date 2025/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The lattices D₄ and E₈ 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 D₄-lattice arises from an infinite family of totally imaginary biquadratic fields. Furthermore, we extend this construction to show that both the D₈ and E₈ can be realized via triquadratic fields derived from this family.

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