Approximating Svp Infinity To Within Almost-Polynomial Factors Is Np-Hard

We show SVPinfinity and CVPinfinity to be NP-hard to approximate to within nc/(log log n) for some constant c > 0. We show a direct reduction from SAT to these problems, that combines ideas from [ABSS93] and from [DKRS99], along with some modifications. Our result is obtained without relying on the PCP characterization of NP, although some of our techniques are derived from the proof of the PCP characterization itself [DFK(+)99].