Some Menon designs having $U(3,3)$ as an automorphism group
Some Menon designs having $U(3,3)$ as an automorphism group
There exists a unique symmetric (36,15,6) design $\mathcal{D}$ having $G'(2,2) \cong U(3,3)$ as an automorphism group. There is an incidence matrix $M$ of $\mathcal{D}$ which is symmetric with $1$ everywhere on the main diagonal. Thus $\mathcal{D}$ admits a polarity for which all points are absolute. Therefore, $M$ is an adjacency …