Exchange interactions between the holes confined in arrays of strained quantum dots subject to compressive and tensile strain are shown to lead to ferrimagnetic arrangement of magnetic moments. Using example of strainedIn1−xGaxAsquantum dots on InP substrate, it is shown how magnetic properties of a semiconductor material can be engineered without resorting to doping with magnetic ions, and the Curie temperature is estimated to be of the order of 25 K. Potential applications in information storage and processing are considered. ©1998 American Institute of Physics.