Construction of E(s2) optimal supersaturated designs using cyclic BIBDs

Liu, Min-Qian; Zhang, Runchu

doi:10.1016/s0378-3758(00)00136-1

Cited by 76 publications

(19 citation statements)

References 8 publications

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“…As already mentioned in Section 1, combinatorial configurations have been proved to be very useful in the constructions of uniform designs, see for example [3,13,14] and references therein. In the process one always takes "discrete discrepancy" as the criterion of uniformity.…”

Section: Constructions Of Uniform Designsmentioning

confidence: 97%

“…Meanwhile, combinatorial configurations have been extensively used to construct uniform designs under the discrete discrepancy (or categorical discrepancy) proposed by Hickernell and Liu [12]. Vital papers include [3][4][5]13,14]. In this paper, we will make use of the wraparound L 2 -discrepancy as the benchmark of uniformity to construct uniform designs via a new class of combinatorial configuration named "perfect resolvable balanced incomplete block design (PRBIBD)".…”

Section: Introductionmentioning

confidence: 99%

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Lower bounds for wrap-around L2-discrepancy and constructions of symmetrical uniform designs

Fang¹,

Tang²,

Yin³

2005

Journal of Complexity

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The wrap-around L 2 -discrepancy has been used in quasi-Monte Carlo methods, especially in experimental designs. In this paper, explicit lower bounds of the wrap-around L 2 -discrepancy of U-type designs are obtained. Sufficient conditions for U-type designs to achieve their lower bounds are given. Taking advantage of these conditions, we consider the perfect resolvable balanced incomplete block designs, and use them to construct uniform designs under the wrap-around L 2 -discrepancy directly. We also propose an efficient balance-pursuit heuristic, by which we find many new uniform designs, especially with high levels. It is seen that the new algorithm is more powerful than existing threshold accepting ones in the literature.

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Section: Constructions Of Uniform Designsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Lower bounds for wrap-around L2-discrepancy and constructions of symmetrical uniform designs

Fang¹,

Tang²,

Yin³

2005

Journal of Complexity

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show abstract

“…Since then, many researchers have investigated the construction of twolevel supersaturated designs. Some important works in this area include [4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Group screening method for the statistical analysis ofE(fNOD)-optimal mixed-level supersaturated designs

Koukouvinos

Mylona

2009

Statistical Methodology

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“…More recently, two new construction methods have been applied, i.e., construction via combinatorial design and construction by stochastic optimization. The first method utilizes the properties of various combinatorial configurations as well as construction techniques frequently used in design theory to obtain uniform designs without any computation (see, for example, [2,3,10,11]). Thus, this method can be used to obtain certain infinite classes of uniform designs.…”

Section: Introductionmentioning

confidence: 99%

Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels

et al. 2005

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Abstract. New lower bounds for three-and four-level designs under the centered L 2 -discrepancy are provided. We describe necessary conditions for the existence of a uniform design meeting these lower bounds. We consider several modifications of two stochastic optimization algorithms for the problem of finding uniform or close to uniform designs under the centered L 2 -discrepancy. Besides the threshold accepting algorithm, we introduce an algorithm named balance-pursuit heuristic. This algorithm uses some combinatorial properties of inner structures required for a uniform design. Using the best specifications of these algorithms we obtain many designs whose discrepancy is lower than those obtained in previous works, as well as many new low-discrepancy designs with fairly large scale. Moreover, some of these designs meet the lower bound, i.e., are uniform designs.

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Construction of E(s2) optimal supersaturated designs using cyclic BIBDs

Cited by 76 publications

References 8 publications

Lower bounds for wrap-around L2-discrepancy and constructions of symmetrical uniform designs

Lower bounds for wrap-around L2-discrepancy and constructions of symmetrical uniform designs

Group screening method for the statistical analysis ofE(fNOD)-optimal mixed-level supersaturated designs

Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels

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