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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Steiner t-Designs for Large t
verfasst von : Michael Huber
Erschienen in: Mathematical Methods in Computer Science
Verlag: Springer Berlin Heidelberg
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One of the most central and long-standing open questions in combinatorial design theory concerns the existence of Steiner
t
-designs for large values of
t
. Although in his classical 1987 paper, L. Teirlinck has shown that non-trivial
t
-designs exist for all values of
t
, no non-trivial Steiner
t
-design with
t
> 5 has been constructed until now. Understandingly, the case
t
= 6 has received considerable attention. There has been recent progress concerning the existence of highly symmetric Steiner 6-designs: It is shown in [M. Huber,
J. Algebr. Comb.
26
(2007), pp. 453–476] that no non-trivial flag-transitive Steiner 6-design can exist. In this paper, we announce that essentially also no block-transitive Steiner 6-design can exist.