Simultaneous packing and covering in sequence spaces

Details Simultaneous packing and covering in sequence spaces Simultaneous packing and covering in sequence spaces

2008-06-27

arxiv.org/abs/0806.4473v1

Mathematics

Metric Geometry

5 pages

Scientific paper

We adapt a construction of Klee (1981) to find a packing of unit balls in
$\ell_p$ ($1\leq p<\infty$) 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.

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