"Quasi‐symmetric 2‐(28, 12, 11) designs with an automorphism of order 7" by Yuan Ding, Sheridan Houghten et al.
 

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.

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

Publication Title

Journal of Combinatorial Designs

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