Maximum scattered Fq-linear sets of PG(1,q4)

There are two known families of maximum scattered Fq-linear sets in PG(1,qt): the linear sets of pseudoregulus type and for t≥4 the scattered linear sets found by Lunardon and Polverino. For t=4 we show that these are the only maximum scattered Fq-linear sets and we describe the orbits of these linear sets under the groups PGL(2,q4) and PΓL(2,q4).