For p at least 2, approximate closest vector search in ell_p norms becomes 2^O(n) (1/epsilon)^(n/2), and for 1<=p<=2 it becomes 2^O(n) (1/epsilon)^(n/p), via a new covering bound from the modulus of smoothness.
Probabilistic Checking of Proofs and Hardness of Approximation Problems
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Covering convex bodies and the Closest Vector Problem
For p at least 2, approximate closest vector search in ell_p norms becomes 2^O(n) (1/epsilon)^(n/2), and for 1<=p<=2 it becomes 2^O(n) (1/epsilon)^(n/p), via a new covering bound from the modulus of smoothness.