Abstract
First, we shall define idempotent orthogonal arrays and notice that idempotent orthogonal array of strength two are idempotent mutually orthogonal quasi-groups. Then, we shall state some properties of idempotent orthogonal arrays.
Next, we shall prove that, starting from an incomplete orthogonal arrayT E∖F based onE andF ⊂ E, from an orthogonal arrayT G based onG = E − F and from an idempotent orthogonal arrayT H based onH, we are able to construct an incomplete orthogonal arrayT (F∪(G×H))∖F based onF∪(G × H) andF.
Finally, we shall show the relationship between the construction which lead us to this result and the singular direct product of mutually orthogonal quasi-groups given by Sade [5].
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Maurin, F. Incomplete orthogonal arrays and idempotent orthogonal arrays. Graphs and Combinatorics 12, 253–266 (1996). https://doi.org/10.1007/BF01858459
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DOI: https://doi.org/10.1007/BF01858459