  The concept of linear set in projective spaces over finite fields was
introduced by Lunardon in 1999 and it plays central roles in the study of
blocking sets, semifields, rank-distance codes and etc. A linear set with the
largest possible cardinality and rank is called maximum scattered. Despite two
decades of study, there are only a limited number of maximum scattered linear
sets of a line $\mathrm{PG}(1,q^n)$. In this paper, we provide a large family
of new maximum scattered linear sets over $\mathrm{PG}(1,q^n)$ for any even
$n\geq 6$ and odd $q$. In particular, the relevant family contains at least
  \[ \begin{cases}
  \left\lfloor\frac{q^t+1}{8rt}\right\rfloor,& \text{ if }t\not\equiv
2\pmod{4};\\[8pt]
  \left\lfloor\frac{q^t+1}{4rt(q^2+1)}\right\rfloor,& \text{ if }t\equiv
2\pmod{4},
  \end{cases} \]
  inequivalent members for given $q=p^r$ and $n=2t>8$, where
$p=\mathrm{char}(\mathbb{F}_q)$. This is a great improvement of previous
results: for given $q$ and $n>8$, the number of inequivalent maximum scattered
linear sets of $\mathrm{PG}(1,q^n)$ in all classes known so far, is smaller
than $q^2$. Moreover, we show that there are a large number of new maximum
rank-distance codes arising from the constructed linear sets.
