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.