Every sum-free set A in F_5^n with |A| at least 28 times 5 to the n-3 is either in two parallel hyperplanes or isomorphic to a specific 28-element sum-free set in F_5^3 times the lower-dimensional space.
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Large sum-free sets in finite vector spaces II
Every sum-free set A in F_5^n with |A| at least 28 times 5 to the n-3 is either in two parallel hyperplanes or isomorphic to a specific 28-element sum-free set in F_5^3 times the lower-dimensional space.