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Bounds on the number of Hadamard designs of even order

✍ Scribed by Clement Lam; Sigmund Lam; Vladimir D. Tonchev

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 183 KB
Volume: 9
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.1017

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✦ Synopsis

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 2__n__ given in [12] by a factor of 8__n__ − 1 for every odd n > 1, and for every even n such that 4__n__ − 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 × 10^15^, and 10^27^, respectively. For orders 2__n__ = 14, 16, 18 and 20, a lower bound of (4__n__ − 1)! is proved. It is conjectured that (4__n__ − 1)! is a lower bound for all orders 2__n__ ≥ 14. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 363‐378, 2001

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