# La Jolla Difference Set Repository

A *(v,k,λ)-difference set in a group G* is
a subset D = {d_{1}, d_{2}, ..., d_{k}} of *G*
such that each nonzero element of G can each be represented
as a difference (d_{i} - d_{j}) in exactly λ different ways.

This page gives information about possible parameters for
difference sets in abelian groups *G*. All parameters with
*v<10000* or *k<300*
passing basic tests (counting, Schutzenberger, BRC) are listed here,
and an attempt has been made to include all known difference sets.
Most known for large *v* are Paley, which are easily constructed,
so those are omitted for *v>1000*.

Some constructions have not been included yet.
If you have any difference sets or
nonexistence results not in this database, or find any errors, please
let me know. The Multiplier
Conjecture link below has information about recent computations for
*v<10*^{6}.

Groups are specified by their elementary divisors or invariant
factors; for example,
(96,20,4)-difference sets in the group
**Z**_{2} ⊕ **Z**_{4} ⊕ **Z**_{4} ⊕ **Z**_{3}
may be found by searching for "2,4,12" or "2,4,4,3".
You can search for cyclic groups by typing "cyclic" in the group
search field.

## Search for difference sets

Maintained by Dan Gordon