Column-orthogonal and nearly column-orthogonal designs for models with second-order terms

• We present the construction of column-orthogonal designs (COD) and nearly column orthogonal designs (NCOD). Our approach uses generalized orthogonal designs, disjoint circulant matrices and periodic Golay pairs for the construction.
• We provide a new multiplier by presenting new directed sequences of length 72. This approach leads to a new multiplication technique, and a new infinite family of COD including optimal-designs of many new orders that could not be constructed by any known method in the literature.
• One important property of the presented designs is that their alias structure is calculated and given in closed form, providing a pre-calculate evaluation of all the designs within this class.
• The new lower bounds provided verify that the constructed designs are optimal, with respect to their alias structure, within the class of column orthogonal designs described.
• The proposed optimal designs have many advantages. They are very easy to construct, have flexible run sizes and accommodate many levels. These advantages make the designs of this paper to be good alternatives for computer experiments.

In this paper, we study U-type, column-orthogonal and nearly column-orthogonal designs. Nearly column-orthogonal designs are very useful in cases where column-orthogonal designs are not known. New designs are obtained which are suitable for screening experiments. In certain cases, the constructed designs are shown to be optimal with respect to their aliased structure. The aliased structures, of U-type, column-orthogonal and nearly column-orthogonal designs, are calculated and presented in closed form. This fact makes the new approach innovating and enables the construction of designs that are different from the designs constructed in the literature. An extended multiplication theorem and new infinite families of column-orthogonal designs are presented using periodic Golay pairs.