No three in line: more than 1.5n points in the n × n grid

Construct, for arbitrarily large n, more than 1.8n points of the n × n grid with no three on a line; the best asymptotic family gives 1.5n.

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "discrete-geometry",
	5	+ "combinatorics"
	6	+ ],
	7	+ "type": "construction",
	8	+ "cover": {
	9	+ "motif": "points",
	10	+ "n": 10
	11	+ },
	12	+ "source": {
	13	+ "key": "frontiermath-open",
	14	+ "name": "FrontierMath: Open Problems",
	15	+ "url": "https://epoch.ai/frontiermath/open-problems/no-three-in-line",
	16	+ "id": "no-three-in-line",
	17	+ "curator": "Epoch AI",
	18	+ "status": "unsolved",
	19	+ "as_of": "2026-10-20",
	20	+ "catalog": "0521c19bbd38"
	21	+ }
	22	+}