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AIMS Mathematics

2026, Volume 11, Issue 6: 18600-18613. doi: 10.3934/math.2026756
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Research article

Flag-transitive symmetric designs and double quasi-symmetric designs with 8-dimensional projective orthogonal group $ P\Omega _8^{\pm}(3) $ as socle

  • 1.
    School of Mathematics, Guangdong University of Education, Guangzhou, Guangdong, 510303, China
  • 2.
    School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, Guangdong, 510320, China
  • 3.
    College of Mathematics and Physics, China Three Gorges University, Yichang, Hubei, 443002, China
  • Published: 24 June 2026

  • MSC : 05B05, 05B25, 20B25, 20D05

  • This paper contributes to the study of flag-transitive symmetric 2-$ (v, k, \lambda) $ designs that admit primitive automorphism groups whose socle is the 8-dimensional orthogonal group $ P\Omega_8^{+}(3) $ or $ P\Omega_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.

    Citation: Delu Tian, Qianfen Liao, Zhilin Zhang, Haiyan Guan, Xingyu Chen. Flag-transitive symmetric designs and double quasi-symmetric designs with 8-dimensional projective orthogonal group $ P\Omega _8^{\pm}(3) $ as socle[J]. AIMS Mathematics, 2026, 11(6): 18600-18613. doi: 10.3934/math.2026756

    Related Papers:

  • This paper contributes to the study of flag-transitive symmetric 2-$ (v, k, \lambda) $ designs that admit primitive automorphism groups whose socle is the 8-dimensional orthogonal group $ P\Omega_8^{+}(3) $ or $ P\Omega_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.



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