  A unified construction of the $H^m$-nonconforming virtual elements of any
order $k$ is developed on any shape of polytope in $\mathbb R^n$ with
constraints $m\leq n$ and $k\geq m$. As a vital tool in the construction, a
generalized Green's identity for $H^m$ inner product is derived. The
$H^m$-nonconforming virtual element methods are then used to approximate
solutions of the $m$-harmonic equation. After establishing a bound on the jump
related to the weak continuity, the optimal error estimate of the canonical
interpolation, and the norm equivalence of the stabilization term, the optimal
error estimates are derived for the $H^m$-nonconforming virtual element
methods.
