Title
Quasi‐symmetric 2‐(28, 12, 11) designs with an automorphism of order 7
Document Type
Article
Publication Date
12-1998
Abstract
All quasi‐symmetric 2‐(28, 12, 11) designs with an automorphism of order 7 without fixed points or blocks are enumerated. Up to isomorphism, there are exactly 246 such designs. All but four of these designs are embeddable as derived designs in symmetric 2‐(64, 28, 12) designs, producing in this way at least 8784 nonisomorphic symmetric 2‐(64, 28, 12) designs. The remaining four 2‐(28, 12, 11) designs are the first known examples of nonembeddable quasi‐symmetric quasi‐derived designs. These symmetric 2‐(64, 28, 12) designs also produce at least 8784 nonisomorphic quasi‐symmetric 2‐(36, 16, 12) designs with intersection numbers 6 and 8, including the first known examples of quasi‐symmetric 2‐(36, 16, 12) designs with a trivial automorphism group.
Publication Title
Journal of Combinatorial Designs
Recommended Citation
Ding, Y.,
Houghten, S.,
Lam, C.,
Smith, S.,
Thiel, L.,
&
Tonchev, V.
(1998).
Quasi‐symmetric 2‐(28, 12, 11) designs with an automorphism of order 7.
Journal of Combinatorial Designs,
6(3), 213-223.
http://doi.org/10.1002/(SICI)1520-6610(1998)6:3<213::AID-JCD3>3.0.CO;2-I
Retrieved from: https://digitalcommons.mtu.edu/math-fp/147
Publisher's Statement
© 1998 John Wiley & Sons, Inc. Publisher’s version of record: https://doi.org/10.1002/(SICI)1520-6610(1998)6:33.0.CO;2-I