Any subset of {0,1,2}^n with density at least (log log log log n)^(-c) contains a combinatorial line of length 3.
On app roximability of satisfiable k-csps: III
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Reasonable Bounds for Combinatorial Lines of Length Three
Any subset of {0,1,2}^n with density at least (log log log log n)^(-c) contains a combinatorial line of length 3.