Essential dimension of simple algebras with involutions

Let $1\le m\le n$ be integers with $m\mathrm{\mid }n$ and $\text{cat}{Alg}_{n,m}$ the class of central simple algebras of degree $n$ and exponent dividing $m$. In this paper, we find new, improved upper bounds for the essential dimension and 2-dimension of $\text{cat}{Alg}_{n,2}$. In particular, we show that ${\text{ed}}_2(\text{cat}{Alg}_{16,2})=24$ over a field $F$ of characteristic different from 2.