2008/01/01 by Hutchison, David, Michael Huber, Pandu Rangan, C +19 · 1 citation
Computer Science · Engineering · Mathematics · #Algebra over a field #Algorithm #Block (permutation group theory) #Block design #Coding (social sciences) #Coding theory #Combinatorial design #Combinatorics #Computability, Logic, AI Algorithms #Computer science #Cryptography #Discrete mathematics #Language of mathematics #Mathematics #Mathematics education #Quantum #Quantum computer #Social science #Sociology #Steiner system #Steiner tree problem #Symbolic computation #Theoretical computer science #Transitive relation #graph theory and CDMA systems #math.CO #math.GR #msc:05B05 #msc:20B25 #msc:51E10
paper · pdf · doi:10.1007/978-3-540-89994-5
9 pages; to appear in: Mathematical Methods in Computer Science 2008, ed. by J.Calmet, W.Geiselmann, J.Mueller-Quade, Springer Lecture Notes in Computer Science
arxiv created 2008/09/18 · openalex publication_date 2008/12/10 · arxiv updated 2018/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
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.