@article{
    KaOs04,
    author = {Kaski, Petteri and {\"O}sterg{\aa}rd, Patric R. J.},
    title = "Enumeration of balanced ternary designs",
    url = "http://dx.doi.org/10.1016/S0166-218X(03)00276-2",
    journal = "Discrete Applied Mathematics",
    number = "1--2",
    abstract = "A $(V, B; \rho_1, \rho_2, R; K, \Lambda)$ balanced ternary design is a pair $(\mathcal{V}, \mathcal{B})$, where $\mathcal{V}$ is a $V$-set of points and $\mathcal{B}$ is a collection of $B$ $K$-multisubsets of $\mathcal{V}$ called blocks, such that each point appears $R$ times in the blocks and no block contains a point with multiplicity greater than two. Each point must appear in $\rho_1$ blocks with multiplicity one and in $\rho_2$ blocks with multiplicity two. Additionally, every pair of distinct points must appear exactly $\Lambda$ times in the blocks of the design. A backtrack search algorithm with isomorph rejection is described and employed to enumerate the balanced ternary designs with $V \leq 10$, $B \leq 30$, and $R \leq 15$ for all but 12 of the 155 possible design classes with these parameters.",
    volume = "138",
    year = "2004",
    keywords = "balanced ternary design, enumeration, orderly algorithm",
    pages = "133--141"
}