For every prime power $q$, there is a cyclic $(q^2+q+1,q+1,1)$ difference set in $\mathbb{Z}/(q^2+q+1)\mathbb{Z}$. Its development is the Desarguesian projective plane $PG(2,q)$.
Knowledge Status
Discrete MathematicsCombinatorics
Discussion
This theorem states that For every prime power q, there is a cyclic (q 2+q+1,q+1,1) difference set in Z/(q 2+q+1)Z.. It records a standard tool for constructing or constraining finite combinatorial designs.