We construct a small set of explicit linear transformations mapping R^n to R^{O(\log n)}, such that the L_2 norm of
any vector in R^n is distorted by at most 1\pm o(1) in at
least a fraction of 1 - o(1) of the transformations in the set.
Albeit the tradeoff between the distortion and the success
probability is sub-optimal compared with probabilistic arguments,
we nevertheless are able to apply our construction to a number of
problems. In particular, we use it to construct an \epsilon-sample
(or pseudo-random generator) for spherical digons in S^{n-1},
for \epsilon = o(1). This construction leads to an oblivious
derandomization of the Goemans-Williamson MAX CUT algorithm and
similar approximation algorithms (i.e., we construct a small set
of hyperplanes, such that for any instance we can choose one of
them to generate a good solution). We also construct an
\epsilon-sample for linear threshold functions on S^{n-1}, for
\epsilon = o(1).