Subspace Evasive Sets

We construct explicit subspace-evasive sets. These are subsets of F-n of size vertical bar F vertical bar((1-epsilon)n) whose intersection with any k-dimensional subspace is bounded by a constant c(k, epsilon). This problem was raised by Guruswami (CCC 2011) as it leads to optimal rate list-decodable codes of constant list size. The main technical ingredient is the construction of k low-degree polynomials whose common set of zeros has small intersection with any k-dimensional subspace.