VC-dimensions of nondeterministic finite automata for words of equal length

Ishigami and Tani studied VC-dimensions of deterministic finite automata. We obtain analogous results for the nondeterministic case by extending a result of Champarnaud and Pin, who proved that the maximal deterministic state complexity of a set of binary words of length $n$ is \[ \sum_{i=0}^n\min(2^i,2^{2^{n-i}}-1). \] We show that for the nondeterministic case, if we fully restrict attention to words of length $n$, then we at most need the strictly increasing initial terms in this sum.