Frontiers of Mathematics in China >
Nonexistence of block-transitive 6-designs
Received date: 12 Apr 2011
Accepted date: 28 Jul 2011
Published date: 01 Oct 2011
Copyright
In this paper, we prove that there are no nontrivial block-transitive 6-designs for k≤100. This supports the long-standing conjecture of Cameron and Praeger that there are no nontrivial block-transitive 6-designs.
Jing CHEN , Weijun LIU . Nonexistence of block-transitive 6-designs[J]. Frontiers of Mathematics in China, 2011 , 6(5) : 835 -845 . DOI: 10.1007/s11464-011-0154-5
1 |
Beth T, Jungnickel D, Lenz H. Design Theory. Cambridge: Cambridge University Press, 1993
|
2 |
Cameron P J, Omidi G R, Tayfeh-Rezaie B. 3-Designs from PGL(2, q). Electron J Combin, 2006, 13, # R50
|
3 |
Cameron P J, Praeger C E. Block-transitive designs I: point-imprimitive Designs. Discrete Math, 1993, 118: 33-43
|
4 |
Cameron P J, Praeger C E. Block-transitive t-designs, II: large t. In: De Clerck F,
|
5 |
Huber M. On the Cameron-Praeger Conjecture. J Combin Theory Ser A, 2010, 117: 196-203
|
6 |
Hughes D R, Poper F C. Design Theory. Cambridge: Cambridge University Press, 1985
|
7 |
Kramer E S, Mesner D M. t-Designs on hypergrphs. Discrete Math, 1976, 15: 263-296
|
8 |
Omidi G R, Pournaki M R, Tayfeh-kezaie B. 3-Designs with block size 6 from PSL(2, q) and their large sets. Discrete Math, 2007, 307: 1580-1588
|
9 |
Ray-Chaudhuri D K, Wilson R M. On t-designs. Osaka J Math, 1975, 12: 737-744
|
10 |
van Leijenhorst D C. Orbits on the projective line. J Combin Theory Ser A, 1981, 31: 146-154
|
/
〈 | 〉 |