  In this paper, we investigate the construction of orthogonal product states
with strong nonlocality in multiparty quantum systems. Firstly, we focus on the
tripartite system and propose a general set of orthogonal product states
exhibiting strong nonlocality in $d\otimes d\otimes d$ quantum system, which
contains $6{{\left( d-1 \right)}^{2}}$ states. Secondly, we find that the
number of the sets constructed in this way could be further reduced. Then using
$4\otimes 4\otimes 4$ and $5\otimes 5\otimes 5$ quantum systems as examples, it
can be seen that when d increases, the reduced quantum state is considerable.
Thirdly, by imitating the construction method of the tripartite system, two
3-divisible four-party quantum systems are proposed, $3\otimes 3\otimes
3\otimes 3$ and $4\otimes 4\otimes 4\otimes 4$, both of which contains fewer
states than the existing ones. Our research gives a positive answer to an open
question raised in [Halder, et al., PRL, 122, 040403 (2019)], indicating that
there do exist fewer quantum states that can exhibit strong quantum nonlocality
without entanglement.
