J. A. Davis, J. Jedwab, and M. Mowbray (1998, Des. Cones Cryptogr. 13, 131-
146) gave two new constructions for semi-regular relative difference sets (
RDSs). They asked if the two constructions could be unified. In this paper,
we show that the two constructions are closely related. In fact, the secon
d construction should be viewed as an extension of the first. Furthermore,
we generalize the second construction to obtain new RDSs. (C) 2001 Academic
Press.