An Abelian planar difference set of order 
exists only for 
a prime power. Gordon (1994)
has verified it to be true for 
.
Prime Power Conjecture
See also
Difference SetExplore with Wolfram|Alpha
References
Gordon, D. M. "The Prime Power Conjecture is True for
."
Elec. J. Combin. 1, No. 1, R6, 1-7, 1994. https://doi.org/10.37236/1186.Referenced on Wolfram|Alpha
Prime Power ConjectureCite this as:
Weisstein, Eric W. "Prime Power Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PrimePowerConjecture.html