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

Abstract

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

19 pages