Row-column arrangements of regular and nonregular fractional factorial two-level designs

Row-column designs involve two crossed blocking factors. We propose three combinatorial criteria and a criterion based on D-efficiency to identify optimal row-column arrangements of fractional factorial two-level designs. We search for such arrangements in complete catalogs of 16-run and 24-run orthogonal arrays of strength 2 with two-level treatment factors and two multi-level blocking factors. One of the combinatorial criteria is a good surrogate for the efficiency-based criterion. For searching similar catalogs of strength-3 orthogonal arrays, we adapt the criteria and conduct a complete search for optimal row-column arrangements in catalogs with 64 and 72 runs.