  The construction of quantum error-correcting codes (QECCs) with good
parameters is a hot topic in the area of quantum information and quantum
computing. Quantum maximum distance separable (QMDS) codes are optimal because
the minimum distance cannot be improved for a given length and code size. The
QMDS codes over mixed alphabets are rarely known even if the existence and
construction of QECCs over mixed alphabets with minimum distance more than or
equal to three are still an open question. In this paper, we define an $m$-QMDS
code over mixed alphabets, which is a generalization of QMDS codes. We
establish a relation between $m$-QMDS codes over mixed alphabets and
asymmetrical orthogonal arrays (OAs) with orthogonal partitions. Using this
relation, we propose a general method to construct $m$-QMDS codes. As
applications of this method, numerous infinite families of $m$-QMDS codes over
mixed alphabets can be constructed explicitly. Compared with existing codes,
the constructed codes have more flexibility in the choice of parameters, such
as the alphabet sizes, length and dimension of the encoding state.
