Steiner System

A Steiner system is a set $X$ of $v$ points, and a collection of subsets of $X$ of size $k$ (called blocks), such that any $t$ points of $X$ are in exactly one of the blocks. The special case $t=2$ and $k=3$ corresponds to a so-called Steiner Triple System. For a Projective Plane, $v=n^2+n+1$, $k=n+1$, $t=2$, and the blocks are simply lines.

See also Steiner Quadruple System, Steiner Triple System.

References

Colbourn, C. J. and Dinitz, J. H. (Eds.) CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, 1996.

Woolhouse, W. S. B. ``Prize Question 1733.'' Lady's and Gentleman's Diary. 1844.