On symmetric 2-(70,24,8) designs with an automorphism of order 6

Sanja Rukavina; Vladimir D. Tonchev

doi:10.3336/gm.58.2.05

paper

On symmetric 2-(70,24,8) designs with an automorphism of order 6

arXiv:2211.01237 · doi:10.3336/gm.58.2.05

Abstract

In this paper we analyze possible actions of an automorphism of order six on a $2$ - $(70, 24, 8)$ design, and give a complete classification for the action of the cyclic automorphism group of order six $G = ⟨ ρ ⟩ ≅ Z_{6} ≅ Z_{2} \times Z_{3}$ where $ρ^{3}$ fixes exactly $14$ points (blocks) and $ρ^{2}$ fixes $4$ points (blocks). Up to isomorphism, there are $3718$ such designs. This result significantly increases the number of known $2$ - $(70, 24, 8)$ designs.

arXiv comment10 pages