  We show that a constant factor approximation of the shortest and closest
lattice vector problem w.r.t. any $\ell_p$-norm can be computed in time
$2^{(0.802 +{\epsilon})\, n}$. This matches the currently fastest constant
factor approximation algorithm for the shortest vector problem w.r.t. $\ell_2$.
To obtain our result, we combine the latter algorithm w.r.t. $\ell_2$ with
geometric insights related to coverings.
