A constraint on the parameters of a balanced incomplete block design. A BIBD is an incidence system on a set $V$ of $v$ points and a family $B$ of $b$ blocks: subsets of points, each of size $k$. It is required that each point be contained in just $r$ blocks and each pair of points in just $\lambda$ blocks.
Fisher's inequality states that $$ b \ge v \ . $$
A symmetric design is one in which equality holds: $b = v$.
- Hall, M. jr, Combinatorial theory Blaisdell (1967) Zbl 0196.02401
Fisher inequality. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fisher_inequality&oldid=37365