论文标题
关于对称的2-（70,24,8）设计，其自动形态为6
On symmetric 2-(70,24,8) designs with an automorphism of order 6
论文作者
论文摘要
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 $G= \langle ρ\rangle \cong Z_6 \cong Z_2 \times Z_3$ where $ρ^3$ fixes exactly $14$ points (blocks) and $ρ^2$修复$ 4 $点（块）。直到同构，有3718美元的此类设计。该结果大大增加了已知$ 2 $ - $（70,24,8）$设计的数量。
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 $G= \langle ρ\rangle \cong Z_6 \cong Z_2 \times Z_3$ 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.
