Approximate $\mathrm{CVP}_{p}$ in time $2^{0.802 \, n}$

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 $2^{(0.802 +ε)\, n}$. 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.