Nonregular designs from Paley’s Hadamard matrices: Generalized resolution, projectivity and hidden projection property

Abstract

Nonregular designs are attractive, as compared with regular designs, not just because they have flexible run sizes but also because of their performances in terms of generalized resolution, projectivity, and hidden projection property. In this paper, we conduct a comprehensive study on three classes of designs that are obtained from Paley’s two constructions of Hadamard matrices. In terms of generalized resolution, we complete the study of Shi and Tang [15] on strength-two designs by adding results on strength-three designs. In terms of projectivty and hidden projection property, our results substantially expand those of Bulutoglu and Cheng [2]. For the purpose of practical applications, we conduct an extensive search of minimum G-aberration designs from those with maximum generalized resolutions and results are obtained for strength-two designs with 36, 44, 48, 52, 60, 64, 96 and 128 runs and strength-three designs with 72, 88 and 120 runs.