  We prove that for an arbitrarily small constant $\eps>0,$ assuming NP$\not
\subseteq$DTIME$(2^{{\log^{O(1/\eps)} n}})$, the preprocessing versions of the
closest vector problem and the nearest codeword problem are hard to approximate
within a factor better than $2^{\log ^{1-\eps}n}.$ This improves upon the
previous hardness factor of $(\log n)^\delta$ for some $\delta > 0$ due to
\cite{AKKV05}.
