Bounds on the number of Hadamard designs of even order
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  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.
Journal of Combinatorial Designs
Bounds on the number of Hadamard designs of even order.
Journal of Combinatorial Designs,
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© 2001 John Wiley & Sons, Inc. Publisher’s version of record: https://doi.org/10.1002/jcd.1017