After test I give you my conclusions and what I found

You have 362880 ways to sort the 9 digits a row and 5 000 billions of billions the 81

But in fact many of the grids are equal: just isomorph of the Sudoku.

And the valid Latin squares?Are they all isomorphs of any?

For me yes but you have a lot of original:

Just for a bloc you have 2 612 735 of dispositions

How to compute thius number?

It's easy you juste have to genrate bloc latin square with the same first row

At the end you have a set of 2 612 735 blocs.

Now take any bloc you want and renumber the digits (icreating an somorphs) to be in the ordeer you chose the result is necessary in your set of 2 613 000

For example if you choose to renumer the first ROW 123456789

It's still possible: you have always the nine digits.

In Fact the principal interest is that you can use this to solve hardest

sudoku

But silence....Wait for the demonstration

This result is interressing also to create.

Papy