LAUSR

We study mutually unbiased bases formed by special entangled basis with fixed Schmidt number 2 (MUSEB2s) in $\mathbb {C}^{3}\otimes \mathbb {C}^{4p} (p\in \mathbb {Z}^{+})$ . Through analyzing the conditions MUSEB2s satisfy, a systematic way of the concrete construction of MUSEB2s in $\mathbb {C}^{3}\otimes \mathbb {C}^{4p}$ is established. A general approach to constructing MUSMEB2s in $\mathbb {C}^{3}\otimes \mathbb {C}^{4p}(p\in \mathbb {Z}^{+})$ from MUSMEB2s in $\mathbb {C}^{3}\otimes \mathbb {C}^{4}$ is also presented. Detailed examples in $\mathbb {C}^{3}\otimes \mathbb {C}^{4}$ , $\mathbb {C}^{3}\otimes \mathbb {C}^{8}$ and $\mathbb {C}^{3}\otimes \mathbb {C}^{12}$ are given. Especially, by choosing special entangled basis with fixed Schmidt number 2 (SEB2) from [J. Phys. A. Math. Theor. 48245301(2015)], the limitation of $3\nmid p$ in [Quantum Inf. Process. 17:58(2018)] is successfully deleted.