Arc-transitive groups of automorphisms of antipodal distance-regular graphs of diameter $3$ in affine case

In this paper, we describe pairs $(\Gamma, G)$, where $\Gamma$ is an antipodal distance-regular graph of diameter $3$ that possesses an arc-transitive group of automorphisms $G$ such that $G$ induces an affine $2$-transitive permutation group on the set of its antipodal classes. As a corollary, we revise and specify a list of necessary conditions for existence of such pairs, and find several new additional necessary conditions in one-dimensional subcase.