Constructions of lattices via biquadratic and triquadratic fields
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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