In this paper of Richard Weiss, he talks about the nonexistence of 8-transitive graphs, and mentions at the very beginning:
We prove that the inequality $s \leq 7$ holds for finite $s$-transitive graphs assuming that the list of known $2$-transitive permutation groups is complete.
The list he means (I think) is the "list of finite $2$-transitive groups with a non-abelian minimal normal subgroup" appearing in this paper by Peter Cameron.
Now my question is, since these papers are nearly forty years old, do we know now if this list is complete? I tried to look it up myself but could not find anything. I am not super informed about the whole topic.
Thanks in advance!