An improvement to the Minkowski‐Hiawka bound for packing superballs

DOI10.1112/S0025579300013231zbMath0606.10028MaRDI QIDQ3744239

N. J. A. Sloane, J. A. Rush

Publication date: 1987

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

lattice packingssphere packingMinkowski-Hlawka boundpackings of superballs

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31)

Related Items

On the construction of dense lattices with a given automorphisms group ⋮ An indexed set of density bounds on lattice packings ⋮ Some results on the asymptotic behaviour of coefficients of large powers of functions ⋮ Compositions of sums of absolute powers ⋮ Lattice points in high-dimensional spheres ⋮ A lower bound on packing density ⋮ New upper bounds for the density of translative packings of three-dimensional convex bodies with tetrahedral symmetry ⋮ Constructive spherical codes near the Shannon bound ⋮ Perfect codes in the \(\ell_p\) metric ⋮ Packing superballs from codes and algebraic curves ⋮ On the packing densities of superballs and other bodies ⋮ Constructive kissing numbers in high-dimensional spaces ⋮ Dense packings from quadratic fields and codes ⋮ Bounds for the \(l_1\)-distance of \(q\)-ary lattices obtained via constructions \(\mathrm D\), \(\mathrm D'\) and \(\overline{\mathrm D}\) ⋮ Exponential improvements for superball packing upper bounds

Cites Work

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• Existence theorems in the geometry of numbers
• Recent bounds for codes, sphere packings and related problems obtained by linear programming and other methods
• Lee Polynomials of Codes and Theta Functions of Lattices
• Sphere Packings and Error-Correcting Codes