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arXiv · 1801.07516

On the Smith normal form of a skew-symmetric D-optimal design of order $n\equiv 2\pmod{4}$

Gary Greaves·Sho Suda
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Abstract

We show that the Smith normal form of a skew-symmetric D-optimal design of order $n\equiv 2\pmod{4}$ 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 $n\equiv 2\pmod{4}$ 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.

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Gary Greaves, Sho Suda. 2018-01-23. On the Smith normal form of a skew-symmetric D-optimal design of order $n\equiv 2\pmod{4}$. https://arxiv.org/abs/1801.07516

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