Unextendible maximally entangled bases in $${\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}$$

The construction of unextendible maximally entangled bases is tightly related to quantum information processing like local state discrimination. We put forward two constructions of UMEBs in \({\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}\)(\(p\le q\)) 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 Guo (Phys Rev A 94:052302, 2016) by two approaches. Two different 48-member UMEBs in \({\mathbb {C}}^{6}\otimes {\mathbb {C}}^{9}\) have been constructed in detail.