Some Orthogonal Main-Effect Plans for Asymmetrical Factorials

Hadamard matrices are used to construct some saturated asymmetrical main-effect plans of types 4 s × 2 t and n × 4 s × 2 t . For Hadamard numbers t and n with t ≤ n and n ≥ 4, I show that there exists a saturated orthogonal 4 t−1 × 2 nt−3t+2 main-effect plan with nt runs. If t and n are Hadamard numbers such that t, n ≥ 4 and t/2 is also a Hadamard number, then there exists a saturated orthogonal n × 4 h−1 × 2 n(t−1)−3(h−1) main-effect plan with nt runs, where h = min(t, n).