Title of article :
TRANSITIVE t-DESIGNS and STRONGLY REGULAR GRAPHS CONSTRUCTED FROM LINEAR GROUPS L(2; q), q ≤ 23
Author/Authors :
Crnković, Dean Department of Mathematics - University of Rijeka, Rijeka, Croatia , Švob, Andrea Department of Mathematics - University of Rijeka, Rijeka, Croatia
Abstract :
Abstract. In this paper we construct transitive 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 t-designs with certain parameter sets. Among others we constructed t-designs with
parameters 2-(55; 10; 4), 3-(24; 11; 495), 3-(24; 12; 5m);m 2 f11; 12; 22; 33; 44; 66; 132g. Furthermore,
we constructed strongly regular graphs admitting a transitive action of the linear groups L(2; q); q ≤ 23.
Keywords :
transitive group , linear group , strongly regular graph , t-design
