We present an efficient algorithmic framework for constructing multi-level
hp-bases that uses a data-oriented approach that easily extends to any number
of dimensions and provides a natural framework for performance-optimized
implementations. We only operate on the bounding faces of finite elements
without considering their lower-dimensional topological features and
demonstrate the potential of the presented methods using a newly written
open-source library. First, we analyze a Fichera corner and show that the
framework does not increase runtime and memory consumption when compared
against the classical p-version of the finite element method. Then, we compute
a transient example with dynamic refinement and derefinement, where we also
obtain the expected convergence rates and excellent performance in computing
time and memory usage