Transversal Design

A transversal design ${\rm TD}_\lambda(k,n)$ of order $n$, block size $k$, and index $\lambda$ is a triple ($V$, $G$, $B$) such that

1. $V$ is a set of $kn$ elements,

2. $G$ is a partition of $V$ into $k$ classes, each of size $n$ (the ``groups''),

3. $B$ is a collection of $k$-subsets of $V$ (the ``blocks''), and

4. Every unordered pair of elements from $V$ is contained in either exactly one group or in exactly $\lambda$ blocks, but not both.

References

Colbourn, C. J. and Dinitz, J. H. (Eds.) CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, p. 112, 1996.