Optimal k-circulant supersaturated designs Sudhir Gupta a,Ã , Katsuo Hisano a , Luis B. Morales b a Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA b IIMAS, Universidad Nacional Auto ´noma de Me´xico, Me ´xico, DF 04510, Mexico article info Article history: Received 10 March 2010 Received in revised form 25 July 2010 Accepted 30 July 2010 Available online 4 August 2010 Keywords: E(f NOD )-optimality Factorial design 1-Rotational balanced incomplete block design abstract Optimal k-circulant supersaturated designs have been constructed in literature using computer intensive methods. A systematic method of construction for multi-level experiments based on balanced incomplete block designs is presented in this paper. The method is also applicable to two-level experiments. Illustrative examples are also given. & 2010 Elsevier B.V. All rights reserved. 1. Introduction Supersaturated designs are important in various fields including computer experiments, software testing, medical, industrial and engineering experiments, and biometric applications. Methods for constructing supersaturated designs for two-level factors have received considerable attention in literature, see Butler et al. (2001) and the references cited therein, among others. Multi-level supersaturated designs have also been studied by several authors, see Liu and Lin (2009) and the references cited therein, among others. Liu and Dean (2004) introduced k-circulant designs and gave their constructions for two-level factors. Georgiou and Koukouvinos (2006) and Koukouvinos et al. (2007) considered multi-level experiments and provided some optimal k-circulant designs through computer searches. Chen and Liu (2008) and Liu and Zhang (2009) investigated the mixed-level set-up and presented some optimal k-circulant designs, also based on computer searches. For two-level factors, optimal supersaturated designs based on cyclic balanced incomplete block designs (BIBDs) were considered by Ngyuen (1996) and Liu and Zhang (2000). As pointed out by Liu and Dean (2004), two-level k-circulant designs include the supersaturated designs of Ngyuen (1996) and Liu and Zhang (2000). Lu et al. (2003) gave a method of constructing optimal multi-level supersaturated designs using BIBDs. However, no systematic method for constructing optimal k-circulant multi-level supersaturated designs is presently available in the literature. The purpose of this paper is to provide a systematic method of constructing optimal k-circulant multi-level supersaturated designs. Two-level designs can also be obtained using the method. The method is based upon resolvable balanced incomplete block designs (RBIBDs) constructed by cyclically developing a set of initial blocks satisfying certain properties. Alternative plans for some of the k-circulant designs of this paper can also be obtained using Lu et al. (2003). However, a comprehensive comparison of optimal k-circulant supersaturated designs presented here with those obtained Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jspi Journal of Statistical Planning and Inference 0378-3758/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jspi.2010.07.019 Ã Corresponding author. E-mail address: sudhir@math.niu.edu (S. Gupta). Journal of Statistical Planning and Inference 141 (2011) 782–786