How many multiplications do small matrix products need?

Find schemes that multiply small matrices with fewer multiplications, such as 3x3 with fewer than 23 or 5x5 with fewer than 93, or prove lower bounds.

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	1	+{
	2	+ "domain": "computer-science",
	3	+ "topics": [
	4	+ "algorithms-complexity",
	5	+ "algebra"
	6	+ ],
	7	+ "type": "construction",
	8	+ "also": [
	9	+ "proof"
	10	+ ],
	11	+ "source": {
	12	+ "key": "fmm-catalogue",
	13	+ "name": "Yet another catalogue of fast matrix multiplication algorithms",
	14	+ "url": "https://fmm.univ-lille.fr/",
	15	+ "curator": "Alexandre Sedoglavic",
	16	+ "status": "open",
	17	+ "as_of": "2026-10-20",
	18	+ "catalog": "0521c19bbd38"
	19	+ }
	20	+}