Counting Balanced Ternary Designs

An inductive process is used to find formulae for the number of 3-block configurations in BTD’s with parameters \((\mathcal{V}; \mathcal{B}; \mathcal{R}, p_1, p_2; 3; 2)\). In the process, a generating set of size nine is produced for the formulae. Because BIBD’s can be viewed as BTD’s with \(p_2 = 0\), once found, the BTD formulae yield the 3-block configuration formulae for BIBD’s with parameters \((v, b, r, 3, 2)\).