Given a finite field $\mathbb F_q$, we say that a set $A\subseteq \mathbb F^n_q$ is an $(r,c)$ subspace evasive set if and only if for any affine subspace $U\subseteq \mathbb F^n_q$ with bounded dimension $\dim(U)\leq r$, the intersection size $|A\cap U|$ is at most $c$. The probabilistic method shows the ... more >>>