  In this work we describe an explicit, simple, construction of large subsets
of F^n, where F is a finite field, that have small intersection with every
k-dimensional affine subspace. Interest in the explicit construction of such
sets, termed subspace-evasive sets, started in the work of Pudlak and Rodl
(2004) who showed how such constructions over the binary field can be used to
construct explicit Ramsey graphs. More recently, Guruswami (2011) showed that,
over large finite fields (of size polynomial in n), subspace evasive sets can
be used to obtain explicit list-decodable codes with optimal rate and constant
list-size. In this work we construct subspace evasive sets over large fields
and use them to reduce the list size of folded Reed-Solomon codes form poly(n)
to a constant.
