by Henk, Martin, Zong, Chuanming.

**Series:** 1999-30, Preprints

- MSC:
- 52C17 Packing and covering in $n$ dimensions

**Abstract:**

Denote by $B^n$ the $n$-dimensional unit ball centred

at ${\bf o}$. It is known that in every lattice packing of $B^n$ there

is a cylindrical hole of infinite length whenever $n\ge 3$. As a

counterpart, this note mainly proves the following result: {\it For

any fixed $\epsilon $, $\epsilon > 0$, there exist a periodic

point set $P(n, \epsilon )$ and a constant $c(n, \epsilon )$ such

that $B^n+P(n, \epsilon )$ is a packing in $R^n$, and the length of the

longest segment contained in $R^n\setminus \{ {\rm int} (\epsilon

B^n)+P(n, \epsilon )\}$ is bounded by $c(n, \epsilon )$ from above.}

Generalizations and applications are presented.}

**Keywords:**

ball packings, periodic packings