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Booth and Cox proposed the E(s2) criterion for constructing two-level supersaturated designs. Nguyen [Technometrics 38 (1996) 69–73] and Tang and Wu [Canad. J. Statist 25 (1997) 191–201] independently derived a lower bound for E(s2). This lower bound can be achieved only when m is a multiple of N−1, where m is the number of factors and N is the run size. We present a method that uses difference families to construct designs that satisfy this lower bound. We also derive better lower bounds for the case where the Nguyen–Tang–Wu bound is not achievable. Our bounds cover more cases than a bound recently obtained by Butler, Mead, Eskridge and Gilmour [J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (2001) 621–632]. New E(s2)-optimal designs are obtained by using a computer to search for designs that achieve the improved bounds.


Sourced from the arxiv e-print version of the article at arXiv:math/0410090v1 [math.ST].

The version of record for this article is freely available in open acces from Project Euclid:
Bulutoglu, D. A., & Cheng, C.-S. (2004). Construction of E(s2)-optimal supersaturated designs. The Annals of Statistics, 32(4), 1662–1678.




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The Annals of Statistics