The densest lattice in twenty-four dimensions

DOI10.1090/S1079-6762-04-00130-1zbMath1062.11044arXivmath/0408174MaRDI QIDQ4681006

Abhinav Kumar, Henry Cohn

Publication date: 14 June 2005

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408174

Mathematics Subject Classification ID

Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Lattice packing and covering (number-theoretic aspects) (11H31) Combinatorial aspects of packing and covering (05B40) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

Related Items (14)

Application of an idea of Voronoĭ to lattice packing, supplement ⋮ Sharper bounds on four lattice constants ⋮ Sphere packing bounds via spherical codes ⋮ Covering and Packing with Spheres by Diagonal Distortion in ℝ n ⋮ Estimates on conjectures of Minkowski and Woods. II ⋮ Hermite’s Constant and Lattice Algorithms ⋮ LLL: A Tool for Effective Diophantine Approximation ⋮ A NEW INEQUALITY FOR THE HERMITE CONSTANTS ⋮ Birthday inequalities, repulsion, and hard spheres ⋮ Lattice packing and covering of convex bodies ⋮ Unnamed Item ⋮ Refined Estimates on Conjectures of Woods and Minkowski ⋮ A survey on spherical designs and algebraic combinatorics on spheres ⋮ Universally optimal distribution of points on spheres

Cites Work

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• Optimality and uniqueness of the Leech lattice among lattices
• Spherical codes and designs
• New bounds on the number of unit spheres that can touch a unit sphere in n dimensions
• New upper bounds on sphere packings. II
• New upper bounds on sphere packings. I
• The minimum values of positive quadratic forms in six, seven and eight variables
• The complete enumeration of extreme senary forms

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