On The Possible Automorphisms of a $3$-$(16,7,5)$ Design

Abstract

The existence question for a $3$-$(16,7,5)$ design is open, In this paper, we examine possible automorphisms of this design. We consider a minimum subset of basic permutations consisting of cycles of prime length $p$ and prove that if a $3$-$(16,7,5)$ design exists, then it is either rigid or admits basic automorphisms with cycles of length $2$ or $3$.