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

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