I need the characterization (up to isomorphism) of non-commutative local rings (with identity) of orders 64 and 128. If you know the characterization or a reference, please let me know.
At the end of the article
A.Z.Anan'in, On representability of a finite local ring, J. of Algebra 228 (2000), no. 2, 417--427 (see also Mathematical Reviews 01i:14018),
it is mentioned that the minimal size of "unknown" finite noncommutative local ring is 256. I mean that one can derive the answer by following constructions presented in the article. Sorry for this incomplete answer: I have no rights to write a comment, whereas a complete answer would require some addtional effort (and I am too lazy for that at the moment).