  In this paper, we investigate the Andr\'e/Bruck-Bose representation of
certain $\mathbb{F}_q$-linear sets contained in a line of $\text{PG}(2,q^t)$.
We show that scattered $\mathbb{F}_q$-linear sets of rank $3$ in
$\text{PG}(1,q^3)$ correspond to particular hyperbolic quadrics and that
$\mathbb{F}_q$-linear clubs in $\text{PG}(1,q^t)$ are linked to subspaces of a
certain $2$-design based on normal rational curves; this design extends the
notion of a circumscribed bundle of conics. Finally, we use these results to
construct optimal higgledy-piggledy sets of planes in $\text{PG}(5,q)$.
