For n up to 186 the paper tabulates exact maximum sizes of 3-free subsets, but its headline large-n comparison uses a sphere variant that is not actually 3-free.
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Finding Large Sets Without Arithmetic Progressions of Length Three: An Empirical View and Survey II
For n up to 186 the paper tabulates exact maximum sizes of 3-free subsets, but its headline large-n comparison uses a sphere variant that is not actually 3-free.