On the construct of "good" sboxes

From the point of security view, it's known that the optimal algebraic immunity, optimal nonlinearity and optimal differential uniformity of a sbox permutation of size 8*8 are 3, 112 and 4 respectively. (it is an open problem whether there exists an 8*8 sbox permutation with differential uniformity 2 or not). We once attempted to construct such a sbox whose algebraic immunity, nonlinearity and differential uniformity approach optimal simultaneously, but we failed. While we attempted to prove that there didn't exist the sboxes whose algebraic immunity, nonlinearity and differential uniformity approach optimal simultaneously, we failed as well. We want to know:
1) Are there permuations from GF(2^n) to GF(2^n) whose algebraic immunity, nonlinearity and differential uniformity approach optimal simultaneously, where n is an even number such that n>= 8?
2) If yes, how to construct them?