Symmetric designs possessing tactical decompositions

Ivica Martinjak; Mario-Osvin Pavčević

doi:10.3934/amc.2011.5.199

Article Contents

2011, Volume 5, Issue 2: 199-208. Doi: 10.3934/amc.2011.5.199

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Symmetric designs possessing tactical decompositions

Ivica Martinjak^1, and
Mario-Osvin Pavčević^1,

1.
University of Zagreb, Faculty of Electrical Engineering and Computing, Department of Applied Mathematics, Unska 3, 10000 Zagreb

Received: April 2010

Revised: October 2010

Published: May 2011

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Abstract

The main aim of this paper is to construct symmetric designs with trivial automorphism groups. Being aware of the fact that an exhaustive search for parameters $(36,15,6)$ and $(41,16,6)$ is still impossible, we assume that these designs admit a tactical decomposition which would correspond to an orbit structure achieved under an action of an automorphism of order $3$. This constraint proves to be fruitful and allows us to classify simultaneously those symmetric designs with mentioned parameters which admit an automorphism of order $3$ as well as to construct new designs with a trivial automorphism group.

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Mathematics Subject Classification: Primary: 05B05.

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