Bounds on the number of Hadamard designs of even order

Authors

Clement Lam, Concordia University
Sigmund Lam, Concordia University
Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

8-2001

Abstract

A new lower bound on the number of non‐isomorphic Hadamard symmetric designs of even order is proved. The new bound improves the bound on the number of Hadamard designs of order 2n given in [12] by a factor of 8n − 1 for every odd n > 1, and for every even n such that 4n − 1 > 7 is a prime. For orders 8, 10, and 12, the number of non‐isomorphic Hadamard designs is shown to be at least 22,478,260, 1.31 × 10¹⁵, and 10²⁷, respectively. For orders 2n = 14, 16, 18 and 20, a lower bound of (4n − 1)! is proved. It is conjectured that (4n − 1)! is a lower bound for all orders 2n ≥ 14.

Publisher's Statement

© 2001 John Wiley & Sons, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.1017

Publication Title

Journal of Combinatorial Designs

Recommended Citation

Lam, C., Lam, S., & Tonchev, V. (2001). Bounds on the number of Hadamard designs of even order. Journal of Combinatorial Designs, 9(5), 363-378. http://doi.org/10.1002/jcd.1017
Retrieved from: https://digitalcommons.mtu.edu/math-fp/136