Let's 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 minimal $(n-1)$-blockings set.

 [Covering finite fields with cosets of subspaces][1]. 

[The Blocking Number of an Affine Space][2] 

In these articles it is proved that minimal $(n-1)$-blocking has $n(q-1)+1$ points. 

I can't find any result about minimal $(n-2)$-blocking sets (even for $AG(n,2)$). I have managed to prove following bounds about $(n-2)$-blocking set in $AG(n,2)$. It has at least $2n-1$ and no more than $3n^{\log_{2} 3}+1$ points.

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

I have also asked following questions related to problem:
http://math.stackexchange.com/questions/869308/blocking-set-for-cosets-of-codimension-2
http://math.stackexchange.com/questions/863592/find-minimal-set-of-cosets-c-so-that-each-2-vectors-in-a-n-are-in-one-cos


  [1]: http://www.sciencedirect.com/science/article/pii/0097316577900012
  [2]: http://ac.els-cdn.com/0097316578900134/1-s2.0-0097316578900134-main.pdf?_tid=a4307ca4-80ca-11e5-b438-00000aab0f6c&acdnat=1446404533_eaabb01608cd39e780dbbd0e451260cb