An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays

Due to run size constraints, near-orthogonal arrays (near-OAs) and supersaturated designs, a special case of near-OA, are considered good alternatives to OAs. This paper shows (i) a combinatorial relationship between a mixed-level array and a nonresolvable incomplete block design (IBD) with varying replications (and its dual, a resolvable IBD with varying block sizes); (ii) the relationship between the criterion E(d2) proposed by Lu and Sun (2001) or E(fNOD) proposed by Fang et al. (2003b) used in the (near-) OA construction and the (M, S)-optimality criterion used in the IBD construction; (iii) the derivation of a tighter bound for E(d2); (iv) how to modify the IBD algorithm of Nguyen (1994) to obtain efficient (near-) OA algorithms. Some new (near-) OAs are presented and some near-OAs are compared with arrays constructed by other authors. Examples showing the use of the constructed arrays are given.