### On the existence of block-transitive combinatorial designs

*Michael Huber*

#### 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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