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Orthogonal Trades and the Intersection Problem for Orthogonal Arrays

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Abstract

This work provides an orthogonal trade for all possible volumes \(N \in \mathbb {Z}^+ \setminus \{1,2,3,4,5,7\}\) for block size 4. All orthogonal trades of volume \(N\leqslant 15\) are classified up to isomorphism for this block size. The intersection problem for orthogonal arrays with block size 4 is solved for all but finitely many possible exceptions.

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Acknowledgments

Computational resources were provided by Queensland Cyber Infrastructure Foundation.

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Authors and Affiliations

  1. Department of Mathematics, Yıldız Technical University, Esenler, 34220, Istanbul, Turkey

    Fatih Demirkale

  2. School of Mathematics and Physics, Centre for Discrete Mathematics and Computing, University of Queensland, St Lucia, 4072, Australia

    Diane M. Donovan

  3. Department of Mathematics, Koç University, 34450, Sarıyer, Istanbul, Turkey

    Selda Küçükçifçi & Emine Şule Yazıcı

Authors
  1. Fatih Demirkale
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  2. Diane M. Donovan
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  3. Selda Küçükçifçi
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  4. Emine Şule Yazıcı
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Corresponding author

Correspondence to Emine Şule Yazıcı.

Additional information

Fatih Demirkale: This work was supported by Scientific and Technological Research Council of Turkey TUBITAK Grant Number: 110T692. Diane M. Donovan: This work was carried out during a scientific visit to Koç University supported by TUBITAK Visiting Scientist program 2221 and also supported by Australian Research Council (Grant Number DP1092868). Selda Küçükçifçi: This work was partially supported by Scientific and Technological Research Council of Turkey TUBITAK Grant Number: 114F505.

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Demirkale, F., Donovan, D.M., Küçükçifçi, S. et al. Orthogonal Trades and the Intersection Problem for Orthogonal Arrays. Graphs and Combinatorics 32, 903–912 (2016). https://doi.org/10.1007/s00373-015-1638-y

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  • DOI: https://doi.org/10.1007/s00373-015-1638-y

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