Two-level designs constructed by concatenating orthogonal arrays of strenght three

Two-level orthogonal arrays of N runs, k factors and a strength of 3 provide suitable fractional factorial designs in situations where many of the main effects are expected to be active, as well as some two-factor interactions. If constructed using the fold-over technique, these designs are called even and allow at most N/2 - 1 interactions to be estimated. For k 48, we develop an algorithm for an optimal concatenation of strength-3 designs involving N/2 runs. Our approach involves column permutations of one of the concatenated designs, as well as sign switches of the elements of one or more columns of that design. We illustrate the potential of the algorithm by generating two-level even-odd designs with 64, 80, 96, 112 and 128 runs involving up to 33 factors. To the best of our knowledge, our designs with 80 and 96 runs involving fewer than 21 and 25 factors, respectively, are novel, just like our 112-run designs involving up to 29 factors. Our even-odd designs outperform or are competitive with the best known designs in terms of the aliasing of two-factor interactions and in terms of the number of estimable two-factor interactions.