It is not known whether NEXP is contained in P/poly. Indeed proving that NEXP is not in P/poly would have some applications in derandomization. 

 1. What is the smallest uniform class C for which one can prove that
    C is not contained in P/poly?
    
 2. Would showing that co-NEXP is not contained in P/poly have some
        other complexity theoretic consequences as in the case NEXP vs P/poly?

Note: I'm aware that $SP_2$ is known not to be contained in $Size[n^k]$ for each fixed constant $k$ (This was also shown for MA with 1 bit of advice). But in this question I'm not interested in results for fixed $k$. I'm really interested in classes which are different from P/Poly, even if these classes are very large.