Mathimagics wrote:Nice work, mate!

Thanks!

Mathimagics wrote:You might have missed the fact (noted in earlier posts in this thread) that we now know that min NTV = 0 (we found a grid with NO transversals), and max NTV = 279 (which occurs in the most canonical, aka {MC} grid).

I wrote about my limits for minimal and maximal number of transversals to show - how far my search results were from known limits (i.e. it's no reason for me to do new random search). NTV = 0 is true minimal number of transversals, but why are you sure that NTV = 279 is maximal number of transversals? Certainly, it can be true, but nobody proves this statement.

Mathimagics wrote:I can also report that my search now has identified the new record low NTV for orthogonal grids as 15. That search has been running for several days and tested 1.5 billion grids so far.

Congratulations! Your search is very fast.

Mathimagics wrote:Can you describe your method for "Bird's orthogonal grids" search? (aka "Orthog SudokuP", or just "OrthogP")

I presume your 1 in 1,000,000 figure means the chances of a grid being SudokuP and having an orthog pair which is also SudokuP ...

I am not sure my understanding is right...

For given (randomly generated) sudoku solution grid I am searching for "Bird's transversals", i.e. 9-cells sets, containing different digits (1-9) such, that each cell is located in separate row, in separate column, in separate box and in separate "P-set" (aka "Bird's transversal").

Then I check found "Bird's transversals" for compatibility and register each set, containing 9 pairwise compatible "Bird's transversals", as solution (i.e. "Bird's Design"). Sudoku solution grid producing at least one "Bird's Design" is counted as "Bird's Design base solution grid" or "Bird's orthogonal grid". So, I found 86 "Bird's Design base solution grids" after scanning 10^8 random grids.

Serg

[Edited. I deleted my wrong example of "Bird's Design" containing no repeating triples. Error was caused by a bug in my searching program. Thanks to Mathimagics, who found an error in my example.]