An Abelian planar Difference Set of order exists only for a Prime Power. Gordon (1994) has verified it to be true for .
See also Difference Set
References
Gordon, D. M. ``The Prime Power Conjecture is True for .'' Electronic J. Combinatorics 1, R6 1-7, 1994.
http://www.combinatorics.org/Volume_1/volume1.html#R6.