We prove that for an arbitrarily small constant $\eps>0,$ assuming NP$\not \subseteq$DTIME$(2^{{\log^{O(1/\epsilon)} n}})$, 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 >>>

The original proof of the PCP Theorem composes a Reed-Muller-based PCP with itself, and then composes the resulting PCP with a Hadamard-based PCP [Arora, Lund, Motwani, Sudan and Szegedy ({\em JACM}, 1998)].
Hence, that proof applies a (general) proof composition result twice.
(Dinur's alternative proof consists of logarithmically many gap ... more >>>