  There are two known families of maximum scattered $\mathbb{F}_q$-linear sets
in $PG(1,q^t)$: the linear sets of pseudoregulus type and for $t\geq 4$ the
scattered linear sets found by Lunardon and Polverino. For $t=4$ we show that
these are the only maximum scattered $\mathbb{F}_q$-linear sets and we describe
the orbits of these linear sets under the groups $PGL(2,q^4)$ and $P\Gamma
L(2,q^4)$.
