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The unextendible product bases (UPBs) are interesting members from the familyof orthogonal product states. In this paper, we investigate the construction of3-qubit UPB with strong nonlocality of different sizes. First, a UPB set in${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{3}}$ of size 12 is presented based onthe Shifts UPB, the structure of which is described by mapping the system to a$3\times 3\times 3$ Rubik's Cube. After observing the orthogonal graph of eachqubit, we provide a general method of constructing UPB in ${{C}^{d}}\otimes{{C}^{d}}\otimes {{C}^{d}}$ of size ${{\left( d-1 \right)}^{3}}+3\left( d-2\right)+1$. Second, for the more general case where the dimensions of qubitsare different, we extend the tile structure to 3-qubit system and propose aTri-tile structure for 3-qubit UPB. Then, by means of this structure, a${{C}^{4}}\otimes {{C}^{4}}\otimes {{C}^{5}}$ system of size 30 is obtainedbased on a ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{4}}$ system. Similarly, wegeneralize this approach to ${{C}^{{{d}_{1}}}}\otimes {{C}^{{{d}_{2}}}}\otimes{{C}^{{{d}_{3}}}}$ system which has a similar composition to ${{C}^{d}}\otimes{{C}^{d}}\otimes {{C}^{d}}$. Our research provides a positive answer to theopen questions raised in [Halder, et al., PRL, 122, 040403 (2019)], indicatingthat there do exist multi-qubit UPBs that can exhibit strong quantumnonlocality without entanglement.

Strong nonlocal sets of UPB