In this chapter we construct dense lattice packings in dimensions 32, 36, 40, 48, 64, 96, ..., 65536, ... using a variety of techniques. The main constructions used are Constructions Af (a more abstract version of Construction A), D (which uses a nested family of codes) and E (a powerful general construction which can be applied recursively). Other methods construct dense lattices from ideals in algebraic number fields. We also construct E 8 and the Leech lattice using icosians.
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© 1988 Springer Science+Business Media New York
Conway, J.H., Sloane, N.J.A. (1988). Algebraic Constructions for Lattices. In: Sphere Packings, Lattices and Groups. Grundlehren der mathematischen Wissenschaften, vol 290. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2016-7_8
DOI: https://doi.org/10.1007/978-1-4757-2016-7_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2018-1
Online ISBN: 978-1-4757-2016-7
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