1-DESIGNS CONSTRUCTED FROM THE GROUPS 𝑃𝑆𝐿2(81) AND 𝑃𝑆𝐿2(89)

In this paper, some designs from the primitive permuta- tion representations of the groups 𝑃𝑆𝐿2(81) and 𝑃𝑆𝐿2(89) are con- structed using the Key-Moori Method 1. We determine the automorphism groups of all the obtained designs and prove that the groups 𝑃𝑆𝐿2(81), 𝑃𝑆𝐿2(81):2, 𝑃𝑆𝐿2(81):2, 𝑃𝐺𝐿2(81), 𝑃∑𝐿2(81), 𝑃Γ𝐿2(81), 𝑃𝑆𝐿2(89) and 𝑃𝑆𝐿2(89):2 appear as the automorphism groups of these constructed designs.