  We study the constructions of nonlocal orthogonal product states in
multipartite systems that cannot be distinguished by local operations and
classical communication. We first present two constructions of nonlocal
orthogonal product states in tripartite systems
$\mathcal{C}^{d}\otimes\mathcal{C}^{d}\otimes\mathcal{C}^{d}~(d\geq3)$ and
$\mathcal{C}^d\otimes \mathcal{C}^{d+1}\otimes \mathcal{C}^{d+2}~(d\geq 3)$.
Then for general tripartite quantum system
$\mathcal{C}^{n_{1}}\otimes\mathcal{C}^{n_{2}}\otimes\mathcal{C}^{n_{3}}$
$(3\leq n_{1}\leq n_{2}\leq n_{3})$, we obtain $2(n_{2}+n_{3}-1)-n_{1}$
nonlocal orthogonal product states. Finally, we put forward a new construction
approach in $\mathcal{C}^{d_{1}}\otimes \mathcal{C}^{d_{2}}\otimes\cdots\otimes
\mathcal{C}^{d_{n}}$ $(d_1,d_2,\cdots d_n\geq3,\, n>6)$ multipartite systems.
Remarkably, our indistinguishable sets contain less nonlocal product states
than the existing ones, which improves the recent results and highlights their
related applications in quantum information processing.
