  We classify, up to conjugation, all automorphisms of Niemeier lattices to
which we can apply Miyamoto's orbifold construction. Using this classification,
we prove that the VOAs obtained in [M] and [SS] are all of holomorphic
non-lattice VOAs which we can obtain by applying the $\mathbb{Z}_3$-orbifold
construction to a Niemeier lattice and its automorphism.
