Construction of mutually unbiased bases in ℂd⊗ℂ2ld'

We study mutually unbiased bases in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$Cd?C2ld?. A systematic way of constructing mutually unbiased maximally entangled bases (MUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'} (l\in {\mathbb {Z}}^{+})$$Cd?C2ld?(l?Z+) from MUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd, k\in {\mathbb {Z}}^+)$$Cd?Cd?(d?=kd,k?Z+) and a general approach to construct mutually unbiased unextendible maximally entangled bases (MUUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^ld'} (l \in {\mathbb {Z}}^{+})$$Cd?C2ld?(l?Z+) from MUUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd+r, 0