Abstract
In this article we prove that there is only one symmetric transversal design STD4[12;3] up to isomorphism. We also show that the order of the full automorphism group of STD4[12; 3] is 25· 33 and Aut STD4[12;3] has a regular subgroup as a permutation group on the point set. We used a computer for our research.
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D. BethT. Jungnickel D. Jungnickel H. Lenz (1986) Design Theory Cambridge University Press Cambridge
C. Suetake (2001) ArticleTitleProjective planes and divisible designs Int. J. Math. Game Theory Algebra 11 IssueID6 15–33
C. Suetake (2004) ArticleTitleThe nonexistence of projective planes of order 12 with a collineation group of order 16 J. Combin. Theory Ser. A 107 21–48 Occurrence Handle10.1016/j.jcta.2004.03.006
C. Suetake, The nonexistence of symmetric transversal designs STD5[15; 3]’s, preprint.
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Communicated by: C.J. Colbourn
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Suetake, C. The Classification of Symmetric Transversal Designs STD4[12; 3]’s. Des Codes Crypt 37, 293–304 (2005). https://doi.org/10.1007/s10623-004-3992-2
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DOI: https://doi.org/10.1007/s10623-004-3992-2