We construct a small set of explicit linear transformations mapping Rn to RO(logn), such that the L2 norm ofany vector in Rn is distorted by at most 1o(1) in atleast a fraction of 1−o(1) of the transformations in the set.Albeit the tradeoff between the distortion and the successprobability is sub-optimal compared with probabilistic arguments,we nevertheless are able to apply our construction to a number ofproblems. In particular, we use it to construct an -sample(or pseudo-random generator) for spherical digons in Sn−1,for =o(1). This construction leads to an obliviousderandomization of the Goemans-Williamson MAX CUT algorithm andsimilar approximation algorithms (i.e., we construct a small setof hyperplanes, such that for any instance we can choose one ofthem to generate a good solution). We also construct an-sample for linear threshold functions on Sn−1, for=o(1).