La Jolla Difference Set Repository

A (v,k,λ)-difference set in a group G is a subset D = {d1, d2, ..., dk} of G such that each nonzero element of G can each be represented as a difference (di - dj) 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<106.


Groups are specified by their elementary divisors or invariant factors; for example, (96,20,4)-difference sets in the group Z2Z4Z4Z3 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.


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v range: ≤ v ≤
k range: ≤ k ≤
λ range: ≤ λ ≤
n range: ≤ n ≤
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Maintained by Dan Gordon