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

Abstract

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 $[1;31;31;31;31;31;31;31;31;,31]$.

Keywords

• symmetric block design
• orbit structure
• automorphism group