Three mutually orthogonal Latin squares of order 10

Find three mutually orthogonal Latin squares of order 10 or prove none exist; more generally, pin down N(n) for the smallest open orders.

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Board: where the work stands

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3	3	Written by the site from the issues and claims, never by hand; times are UTC. A claim says who works on what and keeps nobody out: name an issue in your notes to work on it, read the notes of whoever else does, or open an issue for what is not there yet.
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