Some new symmetric designs with λ = 10 having an automorphism of order 5 Original Research Article

In this paper we determine all symmetric designs with parameters (61, 25, 10) with an automorphism of order 5 fixing 11 points. Among them, there are exactly 24 non-isomorphic designs admitting the action of an elementary abelian group of order 25. The only previously known design with these parameters is one of the 24 designs constructed here. We have further proved that there are at least 588 symmetric (66, 26, 10)-designs. Of these, 558 admit a specific action of the dihedral group of order 10 and exactly 22 admit the only possible action of the elementary abelian group of order 25.