  High-dimensional entanglement promises to greatly enhance the performance of
quantum communication and enable quantum advantages unreachable by qubit
entanglement. One of the great challenges, however, is the reliable production,
distribution and local certification of high-dimensional sources of
entanglement. In this article, we present an optical setup capable of producing
quantum states with an exceptionally high-level of scalability, control and
quality, that, together with novel certification techniques, achieve the
highest amount of entanglement recorded so far. We showcase entanglement in
$32$-spatial dimensions with record fidelity to the maximally entangled state
($F=0.933\pm0.001$) and introduce measurement efficient schemes to certify
entanglement of formation ($E_{oF}=3.728\pm0.006$). Combined with the existing
multi-core fibre technology, our results will lay a solid foundation for the
construction of high-dimensional quantum networks.
