Let 
be a group of group order 
and 
be a set of 
elements of 
. If the set of differences 
contains every nonzero element
of 
exactly 
times, then 
is a 
-difference set in 
of order 
. If 
, the difference set is called planar. The quadratic
residues in the finite field 
form a difference set. If there is a difference set of
size 
in a group 
,
then 
must be a multiple of 
,
where 
is a binomial coefficient.
Gordon maintains an index of known difference sets.
."
Electronic J. Combinatorics 1, No. 1, R6, 1-7, 1994.