论文信息 - Thin Lattice Coverings

Thin Lattice Coverings

Let ^ be a compact body of positive volume in W, star-shaped with respect to an interior point, taken to be the origin. For subsets Q of R, the functional sup lattices A represents the minimum density with which Q. can be covered by a lattice A of translates of S. We obtain an upper bound on «9L(#, Z ). If the attributes of # are supplemented with convexity, write 3fC instead. We also bound above the classical minimum la nice-covering density of Jtf. No symmetry conditions are imposed on # and Jf.

J. A. Rush

[1] C. A. Rogers. Lattice Coverings of Space: The Minkowski–Hlawka Theorem , 1958 .

[2] C. A. Rogers. Lattice coverings of space , 1959 .

[3] W. Schmidt. The measure of the set of admissible lattices , 1958 .

[4] F. Thorne,et al. Geometry of Numbers , 2017, Algebraic Number Theory.

[5] Ina Ruck,et al. USA , 1969, The Lancet.

[6] N. J. A. Sloane,et al. An improvement to the Minkowski-Hiawka bound for packing superballs , 1987 .

[7] W. M. Schmidt,et al. Masstheorie in der Geometrie der Zahlen , 1959 .

[8] Noam D. Elkies,et al. On the packing densities of superballs and other bodies , 1991 .

[9] J. A. Rush. A lower bound on packing density , 1989 .

[10] W. Fischer,et al. Sphere Packings, Lattices and Groups , 1990 .

[11] Gérard D. Cohen,et al. A nonconstructive upper bound on covering radius , 1983, IEEE Trans. Inf. Theory.

[12] Gérard D. Cohen,et al. Good coverings of Hamming spaces with spheres , 1985, Discret. Math..

[13] P. Gritzmann. Lattice covering of space with symmetric convex bodies , 1985 .

[14] C. A. Rogers,et al. An Introduction to the Geometry of Numbers , 1959 .