منابع مشابه
The Amount of Overlapping in Partial Coverings of Space by Equal Spheres
has the limit 8 as the side of the cube C tends to infinity . We confine our attention to systems E for which both limits exist . It is clear that 8 = 0, if no two spheres of the system overlap, i .e . if we have a. packing ; and that, in general, the difference 8-0 is a measure of the amount of overlapping . By well-known results of H . Minkowski [1] and H . F. Blichfeldt [2], the maximum dens...
متن کاملGood coverings of Hamming spaces with spheres
The covering radius problem has been considered by many authors (e.g. [ 1, 5, 61). Finally, let t(n, k) be the minimum possible covering radius for an (n, k) code and k(n, p) the minimum possible dimension of a code with covering radius p. The study of t(n, k) was initiated by Karpovsky. For a survey of these questions, see ]41. The main goal of this paper is to find good linear coverings. The ...
متن کاملA SUFFICIENT CONDITION FOR AN EXTREME COVERING OF n-SPACE BY SPHERES
The problem of finding the most economical coverings of M-dimensional Euclidean space by equal spheres whose centres form a lattice, which is equivalent to a problem concerning the inhomogeneous minima of positive definite quadratic forms, has been discussed recently by Barnes and Dickson [1]. The reader is referred to [1] for a complete background on the problem. Terms and notations used will ...
متن کاملOn the Thinnest Coverings of Spheres and Ellipsoids with Balls in on the Thinnest Coverings of Spheres and Ellipsoids
In this paper, we present some new results on the thinnest coverings that can be obtained in Hamming or Euclidean spaces if spheres and ellipsoids are covered with balls of some radius ε. In particular, we tighten the bounds currently known for the ε-entropy of Hamming spheres of an arbitrary radius r. New bounds for the ε-entropy of Hamming balls are also derived. If both parameters ε and r ar...
متن کاملEmbedded Spheres and 4–manifolds with Spin Coverings
A strategy for constructing an embedded sphere in a 4–manifold realizing a given homology class which has been successfully applied in the past is to represent the class as a first step stably by an embedded sphere, i.e. after adding products of 2–spheres, and to move that sphere back into the original manifold. In this paper, we study under what conditions the first step of this approach can b...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1967
ISSN: 0004-9735
DOI: 10.1017/s1446788700005140