@article{Tian2026, 
author = {Delu Tian and Qianfen Liao and Zhilin Zhang and Haiyan Guan and Xingyu Chen},
title = {Flag-transitive symmetric designs and double quasi-symmetric designs with 8-dimensional projective orthogonal group    P      Ω    8          ±        (  3  ) as socle},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {18600-18613},
keywords = {symmetric design, double quasi-symmetric design, flag-transitive, simple group, projective orthogonal group, partially balanced incomplete block design},
url = {https://www.sciopen.com/article/10.3934/math.2026756},
doi = {10.3934/math.2026756},
abstract = {This paper contributes to the study of flag-transitive symmetric 2-   (  v  ,  k  ,  λ  ) designs that admit primitive automorphism groups whose socle is the 8-dimensional orthogonal group    P      Ω    8          +        (  3  ) or    P      Ω    8          −        (  3  ). We prove that no such design exists. Subsequently, we study the related double quasi-symmetric designs and provide some specific examples. The block intersection numbers of these designs are all relatively large. This paper offers a new approach to the research of double quasi-symmetric designs and symmetric partially balanced incomplete block designs.}
}