Counting Balanced Ternary Designs

Abstract

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 $(v,b,r,3,2)$.