= Balanced incomplete block design
{title2=$(t,b,r,k,\lambda)$}
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= BIBD
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A binary <block design> has $t$ <treatments>, $b$ blocks of size $k<t$, every treatment in $r$ blocks, and every distinct pair in $\lambda$ blocks. Counting occurrences and pairs gives $tr=bk$ and $r(k-1)=\lambda(t-1)$. Its <incidence matrix of a set system> $N$ satisfies $NN^T=(r-\lambda)I+\lambda\mathbf1\mathbf1^T$. For statistical comparison of all treatment effects one also needs connectedness; $\lambda>0$ guarantees it, whereas singleton blocks with $\lambda=0$ do not.
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