Howell Design

Let $S$ be a set of $n+1$ symbols, then a Howell design $H(s,2n)$ on symbol set $S$ is an $s\times s$ array $H$ such that

1. Every cell of $H$ is either empty or contains an unordered pair of symbols from $S$,

2. Every symbol of $S$ occurs once in each row and column of $H$, and

3. Every unordered pair of symbols occurs in at most one cell of $H$.

References

Colbourn, C. J. and Dinitz, J. H. (Eds.) ``Howell Designs.'' Ch. 26 in CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, pp. 381-385, 1996.