We prove that for an arbitrarily small constant \eps>0, assuming NP\not \subseteqDTIME(2^{{\log^{O(1/\epsilon)} n}}), the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than 2^{\log ^{1-\epsilon}n}. This improves upon the previous hardness factor of (\log n)^\delta for some $\delta ... more >>>