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The construction of unextendible maximally entangled bases is tightly relatedto quantum information processing like local state discrimination. We putforward two constructions of UMEBs in $\mathbb {C}^{pd}\otimes \mathbb{C}^{qd}$($p\leq q$) based on the constructions of UMEBs in $\mathbb{C}^{d}\otimes \mathbb {C}^{d}$ and in $\mathbb {C}^{p}\otimes \mathbb{C}^{q}$, which generalizes the results in [Phys. Rev. A. 94, 052302 (2016)] bytwo approaches. Two different 48-member UMEBs in $\mathbb {C}^{6}\otimes\mathbb {C}^{9}$ have been constructed in detail.

Unextendible Maximally Entangled Bases in $\mathbb{C}^{pd}\otimes \mathbb{C}^{qd}$