A new construction lowers the triangle-removal-lemma lower-bound exponent constant from about 0.83 to about 1.66, using a Euclidean-ball sumset estimate.
Elkin, An improved construction of progression-free sets, in SODA 10’ (2010), p
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An improved construction for the triangle removal lemma
A new construction lowers the triangle-removal-lemma lower-bound exponent constant from about 0.83 to about 1.66, using a Euclidean-ball sumset estimate.