A d-maximal subset of the n-letter Hamming cube that contains no unit ball has size at most roughly n^d, and related bounds show all finite d-maximal sets are bounded and finitely many up to isomorphism.
Facets in the Vietoris—Rips complexes of hypercubes
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Maximal sets of a given diameter in Hamming cubes
A d-maximal subset of the n-letter Hamming cube that contains no unit ball has size at most roughly n^d, and related bounds show all finite d-maximal sets are bounded and finitely many up to isomorphism.