A finite point set is extremal exactly when its standard monomials are the same for all lexicographic orders, and it suffices to check only n elimination orders, extending a result by Li, Zhang and Dong to arbitrary fields.
Frankl, Extremal set systems, in: R.L
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Standard monomials and extremal point sets
A finite point set is extremal exactly when its standard monomials are the same for all lexicographic orders, and it suffices to check only n elimination orders, extending a result by Li, Zhang and Dong to arbitrary fields.