A Set of Residues (mod ) such that every Nonzero Residue can be uniquely expressed in the form . Examples include (mod 7) and (mod 13). A Necessary condition for a difference set to exist is that be of the form . A Sufficient condition is that be a Prime Power. Perfect sets can be used in the construction of Perfect Rulers.
See also Perfect Ruler
Guy, R. K. ``Modular Difference Sets and Error Correcting Codes.'' §C10 in
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 118-121, 1994.