A difference set is a set 
of 
elements of a group 
of group
order 
such that the differences 
with 
contain every nonzero element
of 
exactly 
times. It is then called an 
-difference set in 
and has difference set
order 
.
A difference set with 
is called a planar difference set. 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.
."
Elec. J. Combin. 1, No. 1, R6, 1-7, 1994.