For a decade field-tuned quantum criticality in the spin-dimer compound BaCuSi2O6 has been of great interest due to an unconventional dimensional crossover at its quantum critical point (QCP). In order to understand the exciting physics of this possibly frustration-induced effect, it is important to perform a thorough experimental study of the ordered phase and its critical behaviour at very high magnetic fields by neutron diffraction. This study especially timely now because recent ab-initio calculations of the exchange parameters predict unfrustrated, ferromagnetic exchange between quantum spin dimers and challenge our current understanding even of the dominate exchange paths. We apply for beam time on HFM/EXED to detect for the first time the magnetic order of BEC-type and its magnetic field and temperature dependence above 23 T, while in parallel we are in the process of refining the Hamiltonian of the material by detailed INS studies.