On a new class of productive regular Hadamard matrices

We show that for each integer n   for which there is a Hadamard matrix of order 4n4n and 8n2-18n2-1 is a prime number, there is a productive regular Hadamard matrix of order 16n2(8n2-1)216n2(8n2-1)2. As a corollary, by applying a recent result of Ionin, we get many parametrically new classes of symmetric designs whenever either of 4n(8n2-1)-14n(8n2-1)-1 or 4n(8n2-1)+14n(8n2-1)+1 is a prime power.