A Census of \((9;1;3,2)\) Balanced Ternary Designs

A balanced ternary design of order nine with block size three, index two, and \(\rho_2 = 1\) is a collection of multi-subsets of size \(3\) (of type \(\{x, y, z\}\) or \(\{x, x, y\}\)) called blocks, chosen from a \(9\)-set, in which each unordered pair of distinct elements occurs twice, possibly in one block, and in which each element is repeated in just one block. So there are precisely \(9\) blocks of type \(\{x, x, y\}\). We denote such a design by \((9; 1; 3, 2)\) BTD. In this note, we describe the procedures we have used to
determine that there are exactly \(1475\) non-isomorphic \((9; 1; 3, 2)\) BTDs.