Title

The number of designs with geometric parameters grows exponentially

Authors

Dieter Jungnickel, University of Augsburg
Vladimir Tonchev, Michigan Technological UniversityFollow

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 PG_n-1(n, q) grows exponentially. Here we extend this result to the number of 2-designs with the parameters of PG_d (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.

Publisher's Statement

© Springer Science+Business Media, LLC 2009. Publisher’s version of record: https://doi.org/10.1007/s10623-009-9299-6

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