Strong quantum nonlocality with genuine entanglement in an N-qutrit system

In this paper, we construct orthogonal genuinely multipartite entangled bases in ${({\mathbb{C}}^{3})}^{\ensuremath{\bigotimes}N}$ for $N\ensuremath{\ge}3$, where every state is a 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 problem raised by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)]. The strongly nonlocal orthogonal genuinely entangled set we constructed in ${({\mathbb{C}}^{3})}^{\ensuremath{\bigotimes}N}$ contains much fewer quantum states than all known ones. Meanwhile, our results also answer the question given by Wang et al. [Phys. Rev. A 104, 012424 (2021)].