On the Support Size of Null Designs of Finite Ranked Posets

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-designs of the lattice of subspaces of a vector space over a finite field. The lower bound we find gives the tight bound for many important posets including the Boolean algebra, the lattice of subspaces of a vector space over a finite field, whereas the idea of the proofs of the main theorems makes it possible to prove that the lower bounds in the main theorems are not tight for some posets.