Abstract: The generalized resolution was introduced and justified as a criterion for selecting nonregular factorial designs. Although there has been extensive research conducted on other aspects of nonregular designs, few works have investigated the construction of nonregular designs with maximum generalized resolutions, as we do in this study. To date, our knowledge of nonregular designs with maximum generalized resolutions is predominantly computational, except for very few theoretical results. We derive lower bounds on relevant J-characteristics and present the construction results. With the assistance of the lower bounds, many of the constructed designs are shown to have maximum generalized resolutions.

Key words and phrases: Good Hadamard matrix, orthogonal array, Paley construction, tensor product.