On the Smith normal form of a skew‐symmetric <scp>d</scp>‐optimal design of order

DOI10.1002/JCD.21626zbMATH Open1417.05022arXiv1801.07516OpenAlexW2903706907MaRDI QIDQ5225116

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Publication date: 19 July 2019

Published in: (Search for Journal in Brave)

Abstract: We show that the Smith normal form of a skew-symmetric D-optimal design of order $nequiv2pmod4$ is determined by its order. Furthermore, we show that the Smith normal form of such a design can be written explicitly in terms of the order $n$, thereby proving a recent conjecture of Armario. We apply our result to show that certain D-optimal designs of order $nequiv2pmod4$ are not equivalent to any skew-symmetric D-optimal design. We also provide a correction to a result in the literature on the Smith normal form of D-optimal designs.

Full work available at URL: https://arxiv.org/abs/1801.07516

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