The generalized Kronecker sum was used by Wang and Wu (J. Amer. Statist. Assoc. 86 (1991) 450) and Dey and Midha (Statist. Probab. Lett. 28 (1996) 211; Proc. AP Akad. Sci. 5 (2001) 39) to construct mixed orthogonal arrays. We modify their methods to obtain several families of mixed orthogonal arrays. Some new arrays with run size less than 100 are found.