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Transitive t-designs and strongly regular graphs constructed from linear groups L(2, q), q <= 23

In this paper we construct t-designs from the linear groups L(2, q), q <= 23. Thereby we classify t-designs, t >= 2, admitting a transitive action of the linear groups L(2, q), q <= 23, up to 35 points and obtained numerous transitive designs, for 36<= v <= 55. In many cases we proved the existence of designs with certain parameters. Among others we constructed designs with parameters 2-(55, 10, 4), 3-(24, 11, 495), 3-(24, 12, 5m), m \in \{; ; ; 11, 12, 22, 33, 44, 66, 132\}; ; ; . Furthermore, we constructed strongly regular graphs admitting a transitive action of the linear groups L(2, q), q <= 23.

t-design ; Strongly regular graph ; Linear group ; Transitive group

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