Abstract
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.
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© 1999 Springer Science+Business Media New York
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Conway, J.H., Sloane, N.J.A. (1999). Laminated Lattices. In: Sphere Packings, Lattices and Groups. Grundlehren der mathematischen Wissenschaften, vol 290. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6568-7_6
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DOI: https://doi.org/10.1007/978-1-4757-6568-7_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3134-4
Online ISBN: 978-1-4757-6568-7
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