Lets define $k$-blocking set in affine space $AG(n,q)$ a set that meets every coset (translate of subspace) of dimension $k$. 

I have seen a lot work related to $(n-1)$-blockings set. [Covering finite fields with cosets of subspaces][1]. Here is proved that minimal $(n-1)$-blocking has $n(q-1)+1$ points. 

I cant find any result about $(n-2)$-blocking sets. I have managed to get following bounds about $(n-2)$-blocking set in $AG(n,2)$. It has at least $2n-1$ and no more than $3n^{\log_{2} 3}+1$.

I am very interested in the solution of the problem. Does anyone know information about it?


  [1]: http://www.sciencedirect.com/science/article/pii/0097316577900012