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 ." Electronic J. Combinatorics 1, No. 1, R6, 1-7, 1994. http://www.combinatorics.org/Volume_1/Abstracts/v1i1r6.html.Referenced on Wolfram|Alpha
Prime Power ConjectureCite this as:
Weisstein, Eric W. "Prime Power Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrimePowerConjecture.html