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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2010

On the existence of block-transitive combinatorial designs

Abstract

Block-transitive Steiner t-designs form a central part of the study of highly symmetric combinatorial configurations at the interface of several disciplines, including group theory, geometry, combinatorics, coding and information theory, and cryptography. The main result of the paper settles an important open question: There exist no non-trivial examples with t = 7 (or larger). The proof is based on the classification of the finite 3-homogeneous permutation groups, itself relying on the finite simple group classification.
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Dates and versions

hal-00990459 , version 1 (13-05-2014)

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Michael Huber. On the existence of block-transitive combinatorial designs. Discrete Mathematics and Theoretical Computer Science, 2010, Vol. 12 no. 1 (1), pp.123-132. ⟨10.46298/dmtcs.516⟩. ⟨hal-00990459⟩

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