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.
Perfect Difference Set
See also
Perfect RulerExplore with Wolfram|Alpha
References
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.Referenced on Wolfram|Alpha
Perfect Difference SetCite this as:
Weisstein, Eric W. "Perfect Difference Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PerfectDifferenceSet.html