AIMS Mathematics, 2019, 4(4): 1258-1273. doi: 10.3934/math.2019.4.1258.

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On the symmetric block design with parameters (280,63,14) admitting a Frobenius group of order 93

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Prishtina, Avenue “Mother Teresa” 5, 10000 Prishtina, Kosovo

In this paper we have proved that for a putative symmetric block design ${\mathcal D}$ with parameters (280,63,14), admitting a Frobenius group $G=\langle\rho,\mu\vert \rho^{31}=\mu^{3}=1,\rho^\mu=\rho^5\rangle$ of order 93, there are exactly thirteen possible orbit structure up to isomorphism; two with the orbit distribution $[1;31;31;31;93;93]$, eight with the orbit distribution $[1;31;31;31;31;31;31;93]$ and three with the orbit distribution $[1;31;31;31;31;31;31;31;31;,31]$.
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Keywords symmetric block design; orbit structure; automorphism group

Citation: Menderes Gashi. On the symmetric block design with parameters (280,63,14) admitting a Frobenius group of order 93. AIMS Mathematics, 2019, 4(4): 1258-1273. doi: 10.3934/math.2019.4.1258


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