2025/03/17 by Rukavina, Sanja, Tonchev, Vladimir D.
#05B05 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.13722
The largest prime p that can be the order of an automorphism of a 2-(35,17,8) design is p=17, and all 2-(35,17,8) designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2-(35,17,8) designs with automorphisms of odd prime order p<17 were also classified. In this paper we give the classification of all symmetric 2-(35,17,8) designs that admit an automorphism of order p=2. It is shown that there are exactly 11,642,495 nonisomorphic such designs. Furthermore, it is shown that the number of nonisomorphic 3-(36,18,8) designs which have at least one derived 2-(35,17,8) design with an automorphism of order 2, is 1,015,225.