The maximum cardinality of trifferent codes with lengths 5 and 6

A code \(\mathcal{C} \subseteq \{0, 1, 2\}^n\) is said to be trifferent with length \(n\) when for any three distinct elements of \(\mathcal{C}\) there exists a coordinate in which they all differ. Defining \(\mathcal{T}(n)\) as the maximum cardinality of trifferent codes with length \(n\), \(\mathcal{T}(n)\) is unknown for \(n \ge 5\). In this note, we use an optimized search algorithm to show that \(\mathcal{T}(5) = 10\) and \(\mathcal{T}(6) = 13\).