New Symmetric Designs from Regular Hadamard Matrices

For every positive integer m, we construct a symmetric (v, k, λ)-design with parameters v = h((2h−1) 2m−1) h−1 , k = h(2h − 1)2m−1, and λ = h(h − 1)(2h − 1)2m−2, where h = ±3 · 2 and |2h − 1| is a prime power. For m ≥ 2 and d ≥ 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 · 4. Submitted: October 30, 1997; Accepted: November 17, 1997 MR Subject Number: 05B05