Difference Sets

A $(v,k,\lambda)$-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 $\lambda$ different ways.

This database gives information about possible parameters for difference sets in abelian groups $G$. All parameters with $v<100000$ passing basic tests (counting, Schutzenberger, Bruck-Ryser-Chowla) 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 $v>1000$.