I am wondering what generic example there is so that an NFA with n states results into a DFA with $2^n$ states after the conversion by the subset construction. I know there is the example by Hopcroft et al. where the resulting DFA has $2^{n-1}$ states but I am looking for a result with exactly 2^n states.
Thanks in advance.
PS: This is not the same question as An NFA with no equivalent DFA with fewer than $2^n$ states: Example and Proof since there $2^{n-1}$ states suffices but I am looking for $2^n$ states.