New two-variable full orthogonal designs and related experiments with linear regression models

Factorial designs are very important when experiments involve two or more factors and it is desirable to study the main effects and the factor interactions. In this paper, four circulant matrices are used for the construction of orthogonal designs. In particular, it is shown that all 26 two-variable full orthogonal designs OD(52;s1,52-s1)OD(52;s1,52-s1) exist and they can be constructed by four circulants. From these new orthogonal designs one can obtain many inequivalent Hadamard matrices and new saturated two-level factorial designs, with 52 runs, suitable for screening and weighing experiments. Some of these designs are directly applicable in linear models for estimating all the main effects.