One and Two-Block Configurations in Balanced Ternary Designs

In this paper, we count \(n\)-block BTD\((V, B, R, 3, 2)\) configurations for \(n = 1\) and \(2\). In particular, we list all configuration types and determine formulae for the number of \(n\)-block subsets of a design of each type. A small number of the formulae are shown to be dependent solely on the design parameters. The remainder are shown to be dependent on the number of occurrences of two particular two-block configurations as well as the design parameters. Three new non-isomorphic BTD\((9; 33; 5, 3, 11; 3; 2)\) are given that illustrate the independence of certain configurations.