Difference family for a Steiner 2-design
= Difference family for a Steiner 2-design
In a finite additive <group>, a family of $k$-subsets is a difference family of index one if each nonzero <group> element occurs exactly once among all their ordered within-block differences. Translating its <Steiner blocks> by every <group> element gives a <Steiner system> with parameters $2$-$(v,k,1)$: the unique representation of a difference determines the unique translated <Steiner block> through two specified points.