  Local distinguishability of orthogonal product states is an area of active
research in quantum information theory. However, most of the relevant results
about local distinguishability found in bipartite quantum systems and very few
are known in multipartite systems. In this work, we construct a locally
indistinguishable subset in
${\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}\bigotimes{\mathbb{C}}^{2d}$,
$d\geq2$ that contains $18(d-1)$ orthogonal product states. Further, we
generalize our method to arbitrary tripartite quantum systems
${\mathbb{C}}^{k}\bigotimes{\mathbb{C}}^{l}\bigotimes{\mathbb{C}}^{m}$. This
result enables us to understand further the role of nonlocality without
entanglement in multipartite quantum systems. Finally, we prove that a
three-qubit GHZ state is sufficient as a resource to distinguish each of the
above classes of states.
