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

Abstract

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.