New symmetric designs from regular Hadamard matrices (Q1379123)

Summary: For every positive integer \(m\), we construct a symmetric \((v,k,\lambda )\)-design with parameters \(v=\frac{h((2h-1)^{2m}-1)}{h-1}\), \(k=h(2h-1)^{2m-1}\), and \(\lambda =h(h-1)(2h-1)^{2m-2}\), where \(h=\pm 3\cdot 2^d\) and \(|2h-1|\) is a prime power. For \(m\geq 2\) and \(d\geq 1\), these parameter values were previously undecided. The tools used in the construction are balanced generalized weighing matrices and regular Hadamard matrices of order \(9\cdot 4^d\).