On Involutions Acting on Symmetric \((81,16,3)\)-Block Designs

We show that \((81, 16, 3)\)-block designs have no involutionary automorphisms that fix just \(13\) points. Since the nonexistence of \((81, 16, 3)\)-designs with involutionary automorphism fixing \(17\) points has already been proved, it follows that any involution that an \((81, 16, 3)\)-design may have must fix just \(9\) points.