  A set of multipartite orthogonal product states is strongly nonlocal if it is
locally irreducible in every bipartition, which shows the phenomenon of strong
quantum nonlocality without entanglement. It is known that unextendible product
bases (UPBs) can show the phenomenon of quantum nonlocality without
entanglement. Thus it is interesting to investigate the strong quantum
nonlocality for UPBs. Most of the UPBs with the minimum size cannot demonstrate
strong quantum nonlocality. In this paper, we construct a series of UPBs with
different large sizes in $d_A\otimes d_B\otimes d_C$ and $d_A\otimes d_B\otimes
d_C\otimes d_D$ for $d_A, d_B, d_C, d_D\geq 3$, and we also show that these
UPBs have strong quantum nonlocality, which answers an open question given by
Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] and Yuan
\emph{et al.} [Phys. Rev. A \textbf{102}, 042228 (2020)] for any possible three
and four-partite systems. Furthermore, we propose an entanglement-assisted
protocol to locally discriminate the UPB in $3\otimes 3\otimes 4$, and it
consumes less entanglement resource than the teleportation-based protocol. Our
results build the connection between strong quantum nonlocality and UPBs.
