## The Annals of Statistics

- Ann. Statist.
- Volume 32, Number 4 (2004), 1313-1780

### Construction of *E*(*s*^{2})-optimal supersaturated designs

Dursun A. Bulutoglu and Ching-Shui Cheng

#### Abstract

Booth and Cox proposed the *E*(*s*^{2}) 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*(*s*^{2}). 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*(*s*^{2})-optimal designs are obtained by using a computer to search for designs that achieve the improved bounds.

#### Article information

**Source**

Ann. Statist. Volume 32, Number 4 (2004), 1662-1678.

**Dates**

First available: 4 August 2004

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1091626182

**Digital Object Identifier**

doi:10.1214/009053604000000472

**Mathematical Reviews number (MathSciNet)**

MR2089137

**Zentralblatt MATH identifier**

02100827

**Subjects**

Primary: 62K15: Factorial designs

Secondary: 62K10: Block designs

**Keywords**

Balanced incomplete block designs difference families effect sparsity Hadamard matrices

#### Citation

Bulutoglu, Dursun A.; Cheng, Ching-Shui. Construction of E ( s 2 )-optimal supersaturated designs. The Annals of Statistics 32 (2004), no. 4, 1662--1678. doi:10.1214/009053604000000472. http://projecteuclid.org/euclid.aos/1091626182.