  One of the main problems of the research area of network coding is to compute
good lower and upper bounds of the achievable cardinality of so-called subspace
codes in $\operatorname{PG}(n,q)$, i.e., the set of subspaces of
$\mathbb{F}_q^n$, for a given minimal distance. Here we generalize a
construction of Etzion and Silberstein to a wide range of parameters. This
construction, named coset construction, improves or attains several of the
previously best-known subspace code sizes and attains the MRD bound for an
infinite family of parameters.
