See A107739 for definition of an n^2 X n^2 sudoku.
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 13, 46 and 79;
 permutation of blocks of rows 13, 46 and 79;
 permutation of columns 13; permutation of rows 13;
 permutation of columns 46; permutation of rows 46;
 permutation of columns 79; permutation of rows 79.
See A107739 for the total number of ("square") sudoku grids, A114288 for the lexicographically earliest 9 X 9 solution.  M. F. Hasler, Mar 29 2013
