Constructing Hadamard matrices via orthogonal designs

Orthogonal designs were created to give a unifying approach to the construction of Hadamard matrices. Recent work has been concerned with Hadamard matrices of order 2tpq, where t ≤ 5 and one of p and q is small. This paper obtains many new constructions for Hadamard matrices of such orders and works toward a more general construction theory.