there are 6670903752021072936960 sudokugrids from

5472730538 equivalence classes ("S-classes")

where grids are S-equivalent, if they can be transformed into

each other by

permuting symbols

permuting the 3 rows in some stack

permuting the 3 columns in some band

permuting the 3 stacks

permuting the 3 bands

transposing

these 6 groups of transformations do commute and give

9!*6^8*2 transformations in total.

When we omit transposition, we get xxx "T-classes",

xxx S-classes have only 1 T-class, the other S-classes

have 2 T-classes.

there are only 306693 classes ("G-classes"), when we also allow

permuting the 3 entries in any minicolumn but remove transposition.

These 306693 classes generate 11555445688 sudokugrids,

by permuting minicolumns modulo permuting rows in a band,

at least one from each T-class. They can be generated in about

10? minutes but storing them requires too much memory.

Many sudoku-properties are an invariant of the S-class and thus

an invariant of the T-class and can be checked by checking

these 11555445688 generated sudokus.

(planning to fill in the missing numbers later...)

answers and updates to:

http://www.setbb.com/phpbb/viewtopic.php?t=194&mforum=sudoku