In this article, we study symmetric (v,k,λ) designs admitting a flag-transitive and point-primitive automorphism group G whose socle is a projective special unitary group of dimension at most five. We, in particular, determine all such possible parameters (v,k,λ) and show that there exist eight non-isomorphic of such designs for which λ∈{3,6,12,16,18} and G is PSU3(3), PSU3(3):2, PSU4(2) or PSU4(2):2.
@article{arxiv.1912.01065,
title = {Symmetric designs and projective special unitary groups of dimension at most five},
author = {Ashraf Daneshkhah},
journal= {arXiv preprint arXiv:1912.01065},
year = {2019}
}