Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2IVm−p designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some conditions are provided, under which a 2IVm−p design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak minimum aberration 2IVm−p designs are provided for illustrations and two nonisomorphic weak minimum aberration 2IV13−6 designs are constructed at the end of this paper.

This paper is concerned with the uniformity of a certain kind of resolvable incomplete block (RIB for simplicity) design which is called the PRIB design here. A sufficient and necessary condition is obtained, under which a PRIB design is the most uniform in the sense of a discrete discrepancy measure, and the uniform PRIB design is shown to be connected. A construction method for such designs via a kind of U-type designs is proposed, and an existence result of these designs is given. This method sets up an important bridge between PRIB designs and U-type designs.

A uniform design seeks design points that axe uniformly scattared on the experimental domain. It has been popular since 1980. In this paper, we employ the discrete discrepancy as the measure of uniformity for constructing uniform designs. The equivalency among the discrete discrepancy, non-orthogonal measure E (fNoo) and minimum generalized aberration (MGA) for comparing U-type designs U(n; qm) is given. The link between the two apparently unrelated areas of uniform designs and super-simple resolvable L-designs in combinatorial design theory is shown. Through super-simple resolvable t-designs, under the discrete discrepancy, a new method is proposed for constructing uniform designs Un (q,m), in which any of the q2 levelcombinations between any two distinct columns can appear at most twice and any two columns are not fully aliased. Many new uniform designs are obtained.

Supersaturated design is a form of fractional factorial design and has recently received much interest because of its potential in factor screening experiments. This paper mainly concerns the existing criteria for mixed-level designs, i.e. the x2(D) criterion (for design D) proposed by Yamada and Matsui (J. Statist.Plann. Inference 104 (2002) 459), the E (fNOD) criterion proposed by Fang et al. (Metrika 58 (2003b) 279) and the minimum moment aberration (MMA) proposed by Xu (Statist. Sinica 13 (2003) 691). A lower bound of x2(D) is obtained along with the sufficient and necessary condition for achieving it. The connections between x2(D) and other criteria are discussed. Especially, it is shown that x2(D) and the second power moment x2(D) are in fact equivalent to each other and hence the two criteria, x2(D) and MMA, share the same optimal supersaturated designs, which can be constructed from saturated orthogonal arrays and other supersaturated designs.

Incomplete block designs are a type of experimental design layout that has had widespread use in science and engineering. A balanced incomplete block design (BIB) can be characterized by the balanced arrangement of its design points. In this article, incomplete block designs will be investigated from a new perspective: the perspective of uniformity in distribution of design points. A design is of high uniformity, or low discrepancy, if its design points distribute uniformly over the entire design space. The authors use a general discrepancy measure to prove theoretically that BIBs are the most uniform ones among all binary incomplete block designs.

A supersaturated design is essentially a factorial design with the equal occurrence of levels property and no fully aliased factors in which the number of main effects is greater than the number of runs. It has received much recent interest because of its potential in factor screening experiments. A packing design is an important object in combinatorial design theory. In this paper, a strong link between the two apparently unrelated kinds of designs is shown. Several criteria for comparing supersaturated designs are proposed, their properties and connections with other existing criteria are discussed. A combinatorial approach, called the packing method, for constructing optimal supersaturated designs is presented, and properties of the resulting designs are also investigated. Comparisons between the new designs and other existing designs are given, which show that our construction method and the newly constructed designs have good properties.

Combinatorial designs have long had substantial application in the statistical design ofexperiments, and in the theory oferror-correcting codes. Applications in experimental and theoretical computer science, communications, cryptography and networking have also emerged in recent years. In this paper, we focus on a new application of combinatorial design theory in experimental design theory. E(fNOD) criterion is used as a measure ofnon-orthogonality ofU-type designs, and a lower bound of E(fNOD) which can serve as a benchmark ofdesign optimality is obtained. A U-type design is E(fNOD)-optimal ifits E(fNOD) value achieves the lower bound. In most cases, E(fNOD)-optimal U-type designs are supersaturated. We show that a kind of E(fNOD)-optimal designs are equivalent to uniformly resolvable designs. Based on this equivalence, several new in<nite classes for the existence of E(fNOD)-optimal designs are then obtained.

A supersaturated design is essentially a fractional factorial in which the number of potential effects is greater than the number of runs. In this paper, EðfNODÞ criterion is employed for comparing supersaturated designs from the viewpoint of orthogonality and uniformity, and a lower bound of EðfNODÞ which can serve as a benchmark of design optimality is obtained. It is shown that the existing Eðs2Þ and ave v2 criteria (for two- and three-level supersaturated designs respectively) are in fact special cases of this criterion. Furthermore, a construction method for mixed-level supersaturated designs is proposed and some properties of the resulting designs are investigated.

Supersaturated designs have become increasingly popular in recent years because of their potential in saving run size and the technical novelty. In this paper, the minimum generalized aberration (MGA) criterion proposed by Ma and Fang (2001) (and another two equivalent criteria proposed by Xu and Wu (2001) and Xu (2001b) respectively) for comparing non-regular symmetrical designs is used for evaluating supersaturated designs. A new construction method for MGA symmetrical supersaturated designs via resolvable balanced incomplete block designs is proposed, and some infinite classes for the existence of such MGA designs are obtained simultaneously, along with the investigation of properties of the resulting designs. The construction method shows a strong connection between these two different kinds of designs.

Supersaturated designs are factorial designs in which the number of main e ects is greater than the number of experimental runs. In this paper, a discrete discrepancy is proposed as a measure of uniformity for supersaturated designs, and a lower bound of this discrepancy is obtained as a benchmark of design uniformity. A construction method for uniform supersaturated designs via resolvable balanced incomplete block designs is also presented along with the investigation of properties of the resulting designs. The construction method shows a strong link between these two di erent kinds of designs.