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

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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

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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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