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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Computational resources were provided by Queensland Cyber Infrastructure Foundation.
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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