A Note on Lattice Packings via Lattice Refinements
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Publication:5374123
DOI10.1080/10586458.2016.1208595zbMath1388.52011OpenAlexW2522152976MaRDI QIDQ5374123
Publication date: 9 April 2018
Published in: Experimental Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/10586458.2016.1208595
covering radiuslattice packings\(l_p\)-ballslattice densitylattice refinementspacking-covering ratiorunning time algorithm
Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattices and convex bodies (number-theoretic aspects) (11H06) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)
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- Sphere packing bounds via spherical codes
- Improvement on asymptotic density of packing families derived from multiplicative lattices
- Optimality and uniqueness of the Leech lattice among lattices
- Constructive high-dimensional sphere packings
- A lower bound on packing density
- Multiplicative lattices in global fields
- On the packing densities of superballs and other bodies
- New upper bounds on sphere packings. II
- New upper bounds on sphere packings. I
- Simultaneous packing and covering in the Euclidean plane
- A semidefinite programming hierarchy for packing problems in discrete geometry
- The packing density of the \(n\)-dimensional cross-polytope
- The sphere packing problem in dimension 8
- On the construction of dense lattices with a given automorphisms group
- Simultaneous packing and covering in sequence spaces
- The simultaneous packing and covering constants in the plane
- A generalization of Voronoi's reduction theory and its application
- Densest lattice packings of 3-polytopes.
- An introduction to the geometry of numbers.
- Algorithms for the Shortest and Closest Lattice Vector Problems
- On the lattice packing--covering ratio of finite-dimensional normed spaces
- Classification of eight-dimensional perfect forms
- Fast quantizing and decoding and algorithms for lattice quantizers and codes
- SIMULTANEOUS PACKING AND COVERING IN THREE–DIMENSIONAL EUCLIDEAN SPACE
- Almost Perfect Lattices, the Covering Radius Problem, and Applications to Ajtai's Connection Factor
- A Note on Sphere Packings in High Dimension
- Convex and Discrete Geometry
- Faster Deterministic Volume Estimation in the Oracle Model via Thin Lattice Coverings
- Upper bounds for packings of spheres of several radii
- Simultaneous Packing and Covering in Euclidean Space
- Uniformly Convex Spaces
- A Note on Coverings and Packings
- The covering of space by spheres
