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Triple arrays and Youden squares

机译:三重数组和尤登广场

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This paper addresses the question of when triple arrays can be constructed from Youden squares by removing a column together with the symbols therein, and then exchanging the role of columns and symbols. The scope of the investigation is limited to the standard case of triple arrays with . For triple arrays with it is proven that they can never be constructed in this way, and for triple arrays with it is proven that there always exists a suitable Youden square and a suitable column for this construction. Further, it is proven that Youden square constructed from a certain family of difference sets never give rise to triple arrays in this way but always gives rise to double arrays. Finally, it is proven that all triple arrays in the single known infinite family, the Paley triple arrays, can all be constructed in this way for some suitable choice of Youden square and column.
机译:本文解决了以下问题:何时可以从Youden正方形构造三重数组,方法是删除一列及其中的符号,然后交换列和符号的作用。研究的范围仅限于具有λ的三重阵列的标准情况。对于三重阵列,已证明它们永远无法以这种方式构造,对于三重阵列,已证明,始终存在适合此构造的合适的Youden正方形和合适的圆柱。此外,已经证明,由某个差集族构成的尤登广场永远不会以这种方式产生三重阵列,而总会产生双重阵列。最后,事实证明,单个已知无限家族中的所有三重数组,即Paley三重数组,都可以通过这种方式构造,以适合选择Youden正方形和圆柱。

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