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This analysis reveals constructions of the D4 and E8 lattices from biquadratic fields, suggesting new insights into algebraic structures.
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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Santos et al. (2025) studied this question.
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