Construction of asymmetric orthogonal arrays through finite geometries

Suen, Chung-yi; Dey, A.

doi:10.1016/s0378-3758(02)00165-9

Cited by 22 publications

(22 citation statements)

References 1 publication

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“…For completeness, we briefly review the replacement method introduced by Suen et al . . Suppose p is a prime and k ( ⩾ 2) is an integer.…”

Section: A Replacement Methodsmentioning

confidence: 99%

“…Theorem (Suen et al . ). Consider a

t \times \sum_{i = 1}^{n} u_{i}

matrix

A = [A_{1}, A_{2}

\dots, A_{n} false]

A_{i} = false[d_{i 1}, d_{i 2}, \dots, d_{i u_{i}} false]

1 \leq i \leq n

, such that for any choice of g matrices

A_{i_{1}}

A_{i_{2}}

, ⋅⋅⋅,

A_{i_{g}}

from A 1 , A 2 , ⋅⋅⋅,

A_{n}

, the

t \times \sum_{j = 1}^{g} u_{i_{j}}

matrix

[A_{i_{1}}, A_{i_{2}}, \dots, A_{i_{g}}]

has full column rank over

GF (s)

.…”

Section: Introductionmentioning

confidence: 97%

“…Suen et al . proposed a replacement procedure for replacing a column with 2 k symbols in an orthogonal array of strength three by several 2‐symbol columns to obtain new families of tight asymmetric orthogonal arrays of strength three . The replacement procedure of Suen et al .…”

Section: Introductionmentioning

confidence: 99%

“…The replacement procedure of Suen et al . was extended by Suen and Dey . In this paper, we further explore the replacement procedure to obtain several new families of orthogonal arrays of strength three .…”

Section: Introductionmentioning

confidence: 99%

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Construction of Asymmetric Orthogonal Arrays of Strength Three via a Replacement Method

Zhang

Deng

Dey

2017

J of Combinatorial Designs

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“…For completeness, we briefly review the replacement method introduced by Suen et al . . Suppose p is a prime and k ( ⩾ 2) is an integer.…”

Section: A Replacement Methodsmentioning

confidence: 99%

“…Theorem (Suen et al . ). Consider a

t \times \sum_{i = 1}^{n} u_{i}

matrix

A = [A_{1}, A_{2}

\dots, A_{n} false]

A_{i} = false[d_{i 1}, d_{i 2}, \dots, d_{i u_{i}} false]

1 \leq i \leq n

, such that for any choice of g matrices

A_{i_{1}}

A_{i_{2}}

, ⋅⋅⋅,

A_{i_{g}}

from A 1 , A 2 , ⋅⋅⋅,

A_{n}

, the

t \times \sum_{j = 1}^{g} u_{i_{j}}

matrix

[A_{i_{1}}, A_{i_{2}}, \dots, A_{i_{g}}]

has full column rank over

GF (s)

.…”

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Construction of Asymmetric Orthogonal Arrays of Strength Three via a Replacement Method

Zhang

Deng

Dey

2017

J of Combinatorial Designs

Self Cite

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“…An orthogonal array is said to have mixed-levels if r ¿ 2. Mixed-level orthogonal arrays have been used extensively in industrial experiments for quality improvement, and their use in other experimental situations has also been widespread (Suen et al, 2001). Constructions of mixed-level orthogonal arrays have been studied by many authors (see Hedayat et al, 1999;Wang and Wu, 1991;Mandeli, 1995;De Cock and Stufken, 2000;Wang, 1996, etc.).…”

Section: Introductionmentioning

confidence: 99%

Further results on the orthogonal arrays obtained by generalized Hadamard product

Pang

Zhang

Liu

2004

Statistics & Probability Letters

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New results on large sets of orthogonal arrays and orthogonal arrays

Chen,

Niu,

Shi

2024

J of Combinatorial Designs

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Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory, and cryptography. In this paper, some new series of large sets of orthogonal arrays are given by direct construction, juxtaposition construction, Hadamard construction, finite field construction, and difference matrix construction. Subsequently, many new infinite classes of orthogonal arrays are obtained by using these large sets of orthogonal arrays and Kronecker product.

show abstract

Construction of asymmetric orthogonal arrays through finite geometries

Cited by 22 publications

References 1 publication

Construction of Asymmetric Orthogonal Arrays of Strength Three via a Replacement Method

Construction of Asymmetric Orthogonal Arrays of Strength Three via a Replacement Method

Further results on the orthogonal arrays obtained by generalized Hadamard product

New results on large sets of orthogonal arrays and orthogonal arrays

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