  In this paper, we construct genuinely multipartite entangled bases in
$(\mathbb{C}^{3})^{\otimes N}$ for $N\geq3$, where every state is one-uniform
state. By modifying this construction, we successfully obtain strongly nonlocal
orthogonal genuinely entangled sets and strongly nonlocal orthogonal genuinely
entangled bases, which provide an answer to the open problem raised by Halder
$et~al.$
[\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.040403}
{Phy. Rev. Lett. \textbf{122}, 040403 (2019)}]. The strongly nonlocal
orthogonal genuine entangled set we constructed in $(\mathbb{C}^{3})^{\otimes
N}$ contains much fewer quantum states than all known ones. When $N>3$, our
result answers the open question given by Wang $et~al$.
[\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.012424}
{Phys. Rev. A \textbf{104}, 012424 (2021)}].
