Three Affine SL(2,8)-Unitals

Abstract

$\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\operatorname{SL}(2,q)$ on the complement of some block. We introduce three non-classical affine $\operatorname{SL}(2,8)$-unitals and their full automorphism groups. Each of those three affine unitals can be completed to at least two non-isomorphic unitals, leading to six pairwise non-isomorphic unitals of order $8$.