We prove that for an arbitrarily small constant 0,">\eps0 assuming NP DTIME(2logO(1)n) , the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than 2log1−n This improves upon the previous hardness factor of (logn) for some 0">0 due to \cite{Alekhnovich Khot Kindler Vishnoi 05}.