engleski

New 3-designs and 2-designs having U(3, 3) as an automorphism group

In this paper we classify 2-designs and 3- designs with 28 or 36 points admitting a transitive action of the unitary group U(3, 3) on points and blocks. We also construct 2- designs and 3-designs with 56 or 63 points and strongly regular graphs on 36, 63 or 126 vertices having U(3, 3) as a transitive automorphism group. Further, we show that this completes the classification of 3-designs admitting a transitive action of the group U(3, 3), in terms of parameters. A number of the 3- designs and 2-designs obtained in this paper have not been known before up to our best knowledge.

Block design ; 3-design ; Strongly regular graph ; Unitary group ; Transitive group

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