Tone sequences in a frequency hopping arrangement are generated and assigned by advantageously employing a combination of a sequence generator and a sequence assignor to generate sequences and assign them on a time slot by time slot basis. In a transmitter, the sequence generator and sequence assignor, in combination with a user tone assignor are employed to generate and assign tone sequences to a user on a time slot by time slot basis. In a receiver, the sequence generator and sequence assignor, in combination with a user tone identifier are employed to generate sequences and to identify incoming tone sequences to a user on a time slot by time slot basis. Specifically, the sequence assignment in a time slot is such that a prescribed plurality of sequences is assigned to a particular user. This partitioning of the tasks facilitates the use of a sequence generator that generates sequences with the desirable properties of interference and frequency diversity and, which, leaves the task of properly assigning these sequences among one or more users to the sequence assignor. The sequence assignor functions in such a manner that the interference and frequency diversity properties for the one or more users are preserved, and this is further facilitated by assigning sequences in such a manner that they maximally overlap prior assigned sequences. In one embodiment of the invention, a Latin square based sequence is generated in accordance with a first prescribed process. In a second embodiment of the invention, a Latin cube based sequence is generated in accordance with a second prescribed process. In a third embodiment of the invention, a Latin hypercube of prescribed dimension based sequence is generated in accordance with a third prescribed process. In still another embodiment of the invention, the principles of the invention are employed to realize frequency band hopping.