On the Smith normal form of a skew‐symmetric d‐optimal design of order

Abstract

We show that the Smith normal form of a skew‐symmetric D‐optimal design of order n ≡ 20.3em ( mod0.3em 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 ≡ 20.3em ( mod0.3em 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.