Association schemes on triples (ASTs) are higher-dimensional analogues of classical association schemes where the relations and adjacency algebras are ternary instead of binary. Analogous to Schurian association schemes, ASTs arise from the actions of two-transitive groups. In this presentation, we provide the sizes and third valencies of the ASTs obtained from the two-transitive permutation groups. We also determine the intersection numbers of the ASTs obtained from the sporadic two-transitive groups and some subgroups of the affine and projective semilinear groups $A\Gamma L(k,n)$ and $P\Gamma L(k,n)$.

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