  In this paper we construct new optimal hierarchical locally recoverable
codes. Our construction is based on a combination of the ideas of
\cite{ballentine2019codes,sasidharan2015codes} with an algebraic number
theoretical approach that allows to give a finer tuning of the minimum distance
of the intermediate code (allowing larger dimension of the final code), and to
remove restrictions on the arithmetic properties of $q$ compared with the size
of the locality sets in the hierarchy. In turn, we manage to obtain codes with
a wide set of parameters both for the size $q$ of the base field, and for the
hierarchy size, while keeping the optimality of the codes we construct.
