We study the densest lattice packings that can be built up in layers. Start with the 1-dimensional lattice Λ1 of even integer points; at the nth step stack layers of a suitable (n − 1) -dimensional lattice Λ n−1 as densely as possible, keeping the same minimal norm; the result is a laminated lattice Λ n . In this chapter the density of Λ n is determined for n ⩽ 48, all Λ n are found for n ⩽ 25, and at least one Λ n is found for 26 ⩽ n ⩽ 48. The unique Λ24 is the Leech lattice. Denser lattices than Λ n are now known for n ⩾ 30.
KeywordsMinimal Norm Integer Point Deep Hole Congruence Class Dimensional Lattice
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