We study the problem of constructing highly nonlinear vectorial maps $F: \mathbb{F}_2^n \to \mathbb{F}_2^m$.
Concretely, we want an $F$ and an $A = A(m,n)>0$ as small as possible, so that for every affine map $L: \mathbb{F}_2^n \to \mathbb{F}_2^m$ (of the form $L(x) = Mx + b$) we have:
$$
agree(F,L) ... more >>>