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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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "combinatorics"
	5	+ ],
	6	+ "type": "construction",
	7	+ "also": [
	8	+ "proof"
	9	+ ],
	10	+ "source": {
	11	+ "key": "mols-handbook",
	12	+ "name": "MOLS table, Handbook of Combinatorial Designs (with updates by J. H. Dinitz)",
	13	+ "url": "https://site.uvm.edu/jdinitz/?p=389",
	14	+ "id": "N(10)",
	15	+ "curator": "Charles J. Colbourn and Jeffrey H. Dinitz",
	16	+ "status": "open",
	17	+ "as_of": "2026-10-20",
	18	+ "catalog": "0521c19bbd38"
	19	+ }
	20	+}