A random construction produces a no-three-collinear set in Z squared with Omega(n over square root of log n) points inside [n] squared, improving the prior lower bound by a square root of log n factor.
Roth,On a problem of Heilbronn, Journal of the London Mathematical Society1(1951), no
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A note on the extensible no-three-in-line problem
A random construction produces a no-three-collinear set in Z squared with Omega(n over square root of log n) points inside [n] squared, improving the prior lower bound by a square root of log n factor.