The most canonical sudoku below needs at least 20 hints to solve.

123456789456789123789123456231564897564897231897231564312645978645978312978312645

It can be first permutated locally to

216543897543789126798126543162435789435897261987261435621354978354978612879612354

with mainly two digits swaps

Then further permutated locally to

793216845518734926246958713965187234187342569432569187379621458851473692624895371

with three digits swaps

Use checker to run this permutated sodoku for about two hours and five sodokus with 19 hints have already been found.

700200800500700000006000710000007000080040009030500000000001000000000602020090000

700200800500700000006000013000007000080040009030500000000001000000000602020090000

700200800500700000006000010000007000080040009030500007000001000000000602020090000

700200800500700000000008003000000000080040560032009000000000400000000002600090001

700200800500030900006000010000007034080000000000500007000001000000000602020090000

The problem is how to permutate the canonical sudoku each time to reduce the number of hints needed. Finally it may possibley solve the minimum hint problem.

I suspect that any permutation will produce a non-isomorphic sudokus. The question will be: is it possible to produce its isomorphic sudokus through a series of permutations. If it is the case, I strongly favour that all Sudokus can be tranformed into each other.

It is quite sensible to perform the permutations within the unavoidable sets. I also notice that permutating three digits in all 9*9 grids can produce lots of permutation variations.