  Strong nonlocality, proposed by Halder {\it et al}.
[\href{https://doi.org/10.1103/PhysRevLett.122.040403}{Phys. Rev. Lett.
\textbf{122}, 040403 (2019)}], is a stronger manifestation than quantum
nonlocality. Subsequently, Shi {\it et al}. presented the concept of the
strongest nonlocality [\href{https://doi.org/10.22331/q-2022-01-05-619}{Quantum
\textbf{6}, 619 (2022)}].
  Recently, Li and Wang
[\href{https://doi.org/10.22331/q-2023-09-07-1101}{Quantum \textbf{7}, 1101
(2023)}] posed the conjecture about a lower bound to the cardinality of the
strongest nonlocal set $\mathcal{S}$ in $\otimes _{i=1}^{n}\mathbb{C}^{d_i}$,
i.e., $|\mathcal{S}|\leq \max_{i}\{\prod_{j=1}^{n}d_j/d_i+1\}$. In this work,
we construct the strongest nonlocal set of size $d^2+1$ in
$\mathbb{C}^{d}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we
obtain the strongest nonlocal set of size $d_{2}d_{3}+1$ in
$\mathbb{C}^{d_1}\otimes \mathbb{C}^{d_2}\otimes \mathbb{C}^{d_3}$. Our
construction reaches the lower bound, which provides an affirmative solution to
Li and Wang's conjecture. In particular, the strongest nonlocal sets we present
here contain the least number of orthogonal states among the available results.
