A list of boolean functions

Address function: $\textrm{Addr}_k: \{\pm 1\}^{k + 2^k} \rightarrow \{\pm 1\}$ is defined by \[ \textrm{Addr}_k(x_1, \ldots, x_k, y_1, \ldots, y_{2^k}) = y_x \] where $x = (x_1, \ldots, x_k)$ is interpreted as a number in $[2^k]$.

A question from boss

Can one efficiently enumerate the orbits of all n-bit Boolean functions under the $S_n$ action (i.e. listing one element from each orbit)?