See A107739 for definition of an n^2 X n^2 sudoku.
a(2) = 2 independently computed by Gary McGuire and Hugo van der Sanden.
For the 9 X 9 case the allowed equivalences are (see link to Jarvis et al.):
- relabeling entries; reflection; rotation;
- permutation of blocks of columns 1-3, 4-6 and 7-9;
- permutation of blocks of rows 1-3, 4-6 and 7-9;
- permutation of columns 1-3; permutation of rows 1-3;
- permutation of columns 4-6; permutation of rows 4-6;
- permutation of columns 7-9; permutation of rows 7-9.
See A107739 for the total number of ("square") sudoku grids, A114288 for the lexicographically minimal 9 X 9 solution. - M. F. Hasler, Mar 29 2013