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Latin Square Trick That Blew My Mind
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Okay, something wrong with formatting in code tag. I tried to fix it and I was told that something went wrong with my input and that I needed to go back and fix it. Herm. So, I'm just going to let it stand for the time being. So, humping along, I coded my LS/Ortho expansion code real nice and parametric like. I can toss anything at it and will do my bidding. It does everything that I described above. But as soon as I tried to go bigger, it broke. I was hopeful that it would work, but I wasn't surprised at all. There is a small domain phenom that I have seen plenty of times before. When things are small, things work just fine and are "self-solving". But bigger sizes means more complexity and more prone to breakage. There are some tricks that work in 4d for sizes 3 and 4 that work just fine and are indeed self-solving. But trying to go bigger and things really do start to break. The rules become more complex. Not to meantion the even/2^n/odd/prime number thing. The structures for a latin square with an even size are vastly different than a latin square with an odd size. And then there are latin squares with the size of a prime number. And also for 2^n (xor). *Very* different structures and patterns. That is why I was so surpised when I took orthos of size 3 (prime number) and managed to make MOLS of size 4 (size 2^n). That is also why I wasn't surprised that I couldn't get bigger (complexity). So, I made some 5x5 "orthos" (invaled orthos) and took out the naughty parts. For 5x5 using above technique we get this: [code] 3 1 2 4 0 . 1 2 . . 0 00 1 4 3 0 2 1 . 3 0 . . 1 11 0 2 0 4 1 3 2 . . 1 . 2 22 3 0 4 1 3 2 0 . . 3 . 3 33 2 1 2 3 0 4 . . . . . [/code] I don't expect anybody to be able to follow that sequence of data because it is my data in my head. Just by looking at the first 5x5 square I know that things aren't right. The other two squares of data just confirm it. I can't fix it to work. Looks like I do have a one-trick pony on my hands that only works in a small domain. And I have absolutely zero idea if I can eventually understand it and manipulate it to work. But I do know that this has led to an ever so slightly deeper understanding of these things. Maybe someday. Cheers.
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