Let G be an automorphism group of a nontrivial t-(k^2,k,\lambda) design. In this paper, we prove that if G is block-transitive, then the socle of G cannot be a finite simple exceptional group of Lie type.
@article{arxiv.2508.18660,
title = {Block-transitive t-(k^2,k,\lam) designs and simple exceptional groups of Lie type},
author = {Xingyu Chen and Haiyan Guan},
journal= {arXiv preprint arXiv:2508.18660},
year = {2025}
}