A Note on Lattice Packings via Lattice Refinements

No abstract is available for this paper.

• Publication year

  2018

• Venue

  Experimental Mathematics

• Publication date

  2018-01-02

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1080/10586458.2016.1208595
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Geometry of Numbers

  2017cited by this paper
• A Short Course On Banach Space Theory

  2016cited by this paper
• The sphere packing problem in dimension 8The sphere packing problem in dimension 8

  2016cited by this paper
• Faster Deterministic Volume Estimation in the Oracle Model via Thin Lattice Coverings

  2015influential reference
• The Packing Density of the $$n$$n-Dimensional Cross-Polytope

  2015cited by this paper
• A FORMAL PROOF OF THE KEPLER CONJECTURE

  2015cited by this paper
• Improvement on asymptotic density of packing families derived from multiplicative lattices

  2015cited by this paper
• A semidefinite programming hierarchy for packing problems in discrete geometry

  2013cited by this paper
• A Note on Sphere Packings in High Dimension

  2013cited by this paper
• Efficient linear programming algorithm to generate the densest lattice sphere packings.

  2013cited by this paper
• Upper bounds for packings of spheres of several radii

  2012cited by this paper
• SPHERE PACKING BOUNDS VIA SPHERICAL CODES

  2012cited by this paper
• Algorithms for the Shortest and Closest Lattice Vector Problems

  2011cited by this paper
• Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming.

  2010cited by this paper
• Dense packings of polyhedra: Platonic and Archimedean solids.

  2009cited by this paper
• Optimal packings of superballs.

  2009cited by this paper
• Et al

  2008cited by this paper
• The simultaneous packing and covering constants in the plane

  2008influential reference
• Simultaneous Packing and Covering in Sequence Spaces

  2008cited by this paper
• Computational geometry of positive definite quadratic forms : polyhedral reduction theories, algorithms, and applications

  2008cited by this paper
• A Generalization of Voronoi's . . .

  2007cited by this paper
• Classification of eight dimensional perfect forms

  2006influential reference
• A generalization of Voronoi's reduction theory and its application

  2006cited by this paper
• On the construction of dense lattices with a given automorphism group

  2006cited by this paper
• Optimality and uniqueness of the Leech lattice among lattices

  2004cited by this paper
• Almost Perfect Lattices, the Covering Radius Problem, and Applications to Ajtai's Connection Factor

  2004influential reference
• A short course on Banach space theory

  2004cited by this paper
• Simultaneous Packing and Covering in Three–Dimensional Euclidean Space

  2003cited by this paper
• Simultaneous Packing and Covering in the Euclidean Plane

  2002cited by this paper
• New upper bounds on sphere packings II

  2001cited by this paper
• New upper bounds on sphere packings I

  2001cited by this paper
• Densest lattice packings of 3-polytopes

  1999cited by this paper
• Sphere packings, I

  1998influential reference
• Finite and infinite packings.

  1994influential reference
• A lower bound for the optimal density of lattice packings

  1992influential reference
• On the packing densities of superballs and other bodies

  1991cited by this paper
• On the lattice packing--covering ratio of finite-dimensional normed spaces

  1990influential reference
• Multiplicative lattices in global fields

  1990cited by this paper
• A lower bound on packing density

  1989influential reference
• On lattice packing of convex symmetric sets in ℜn

  1987influential reference
• Constructive high-dimensional sphere packings

  1987cited by this paper
• Fast quantizing and decoding and algorithms for lattice quantizers and codes

  1982cited by this paper
• Simultaneous Packing and Covering in Euclidean Space

  1972cited by this paper
• An Introduction to the Geometry of Numbers

  1959cited by this paper
• On Uniformly Convex Spaces

  1953cited by this paper
• The covering of space by spheres

  1952influential reference
• A Note on Coverings and Packings

  1950influential reference
• Uniformly convex spaces

  1936cited by this paper
• Berlin

  1855cited by this paper

• The simultaneous lattice packing-covering constant of octahedra

  2023cites this paper
• Packings, sausages and catastrophes

  2020cites this paper