Simultaneous packing and covering in sequence spaces

Abstract

We adapt a construction of Klee (1981) to find a packing of unit balls in ${\ell }_p$ ($1\le p<\infty$) which is efficient in the sense that enlarging the radius of each ball to any $R>2^{1-1/p}$ covers the whole space. We show that the value $2^{1-1/p}$ is optimal.

5 pages

References in corpus (1)

• Computational Approaches to Lattice Packing and Covering Problems

Cited by in corpus (1)

• Density bounds for outer parallel domains of unit ball packings