Orthogonal Designs of Kharaghani Type: \(I\)

Abstract

We use an array given in H. Kharaghani, “Arrays for orthogonal designs”, J. Combin. Designs, \(8 (2000), 166-173\), to obtain infinite families of \(8\)-variable Kharaghani type orthogonal designs, \(OD(8t; k_1, k_1, k_1, k_1, k_2, k_2, k_2, k_2)\), where \(k_1\) and \(k_2\) must be the sum of two squares. In particular, we obtain infinite families of \(8\)-variable Kharaghani type orthogonal designs, \(OD(8t; k, k, k, k, k, k, k, k)\). For odd \(t\), orthogonal designs of order \(\equiv 8 \pmod{16}\) can have at most eight variables.