The number of designs with geometric parameters grows exponentially
Document Type
Article
Publication Date
5-2010
Abstract
It is well-known that the number of 2-designs with the parameters of a classical point-hyperplane design PGn-1(n, q) grows exponentially. Here we extend this result to the number of 2-designs with the parameters of PGd (n, q), where 2 ≤ d ≤ n − 1. We also establish a characterization of the classical geometric designs in terms of hyperplanes and, in the special case d = 2, also in terms of lines. Finally, we shall discuss some interesting configurations of hyperplanes arising in designs with geometric parameters.
Publication Title
Designs, Codes and Cryptography
Recommended Citation
Jungnickel, D.,
&
Tonchev, V.
(2010).
The number of designs with geometric parameters grows exponentially.
Designs, Codes and Cryptography,
55(2-3), 131-140.
http://doi.org/10.1007/s10623-009-9299-6
Retrieved from: https://digitalcommons.mtu.edu/math-fp/99
Publisher's Statement
© Springer Science+Business Media, LLC 2009. Publisher’s version of record: https://doi.org/10.1007/s10623-009-9299-6