Exponential bounds on the number of designs with affine parameters
Document Type
Article
Publication Date
9-29-2010
Abstract
It is well‐known that the number of designs with the parameters of a classical design having as blocks the hyperplanes in PG(n, q) or AG(n, q), n≥3, grows exponentially. This result was extended recently [D. Jungnickel, V. D. Tonchev, Des Codes Cryptogr, published online: 23 May, 2009] to designs having the same parameters as a projective geometry design whose blocks are the d‐subspaces of PG(n, q), for any 2≤d≤n−1. In this paper, exponential lower bounds are proved on the number of non‐isomorphic designs having the same parameters as an affine geometry design whose blocks are the d‐subspaces of AG(n, q), for any 2≤d≤n−1, as well as resolvable designs with these parameters. An exponential lower bound is also proved for the number of non‐isomorphic resolvable 3‐designs with the same parameters as an affine geometry design whose blocks are the d‐subspaces of AG(n, 2), for any 2≤d≤n−1. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 475–487, 2010.
Publication Title
Journal of Combinatorial Designs
Recommended Citation
Clark, D. C.,
Jungnickel, D.,
&
Tonchev, V.
(2010).
Exponential bounds on the number of designs with affine parameters.
Journal of Combinatorial Designs,
18(6), 475-487.
http://doi.org/10.1002/jcd.20256
Retrieved from: https://digitalcommons.mtu.edu/math-fp/100
Publisher's Statement
© 2010 Wiley Periodicals, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.20256