Symmetric balanced incomplete block design
= Symmetric balanced incomplete block design
{title2=$b=t,\quad r=k$}
A <balanced incomplete block design> is symmetric when its number of blocks equals its number of treatments. The identity $bk=tr$ then gives $r=k$. Its square <incidence matrix of a set system> $N$ obeys $NN^T=(r-\lambda)I+\lambda J$, with eigenvalues $r-\lambda$ of multiplicity $t-1$ and $r^2$ of multiplicity one.