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tokens: the microlensing detection (e.g. Alcock et al. 2000 ), halo white dwarfs have been suggested as natural candidates to contribute to the dark matter content of the Galaxy (e.g. Oppenheimer et al. 2001 ). An intense debate arose on this issue, although later studies demonstrated that the white dwarf contribution to dark matter was rather limited (e.g. Torres et al. 2002 ; Flynn, Holopainen Holmberg 2003 ; García-Berro et al. 2004 ; Kilic et al. 2004 ; Bergeron et al. 2005 ). In any case, the search for white dwarfs in the Galactic halo has proven to be a difficult endeavour. In this sense, the intrinsic faintness and the low space density of halo white dwarfs, along with their high surface gravity, which erases any trace on metal content from their atmospheres and disables accurate radial velocity measurements due to the broadening of the Balmer lines, are some of the main factors that have hindered the discovery of suitable candidates. Consequently, during decades, the identification of halo members has relied on the search of cool objects in high proper motion surveys (e.g. Monet et al. 2000 ; Nelson et al. 2002 ; Hall et al. 2008 ; Catalán et al. 2012 ; Munn et al. 2016 ). It was not until the ESO SNIa Progenitor surveY project (see Napiwotzki et al. 2020 , and references therein) that radial velocities were measured for the first time with enough precision to recover the 3D kinematics of white dwarfs. That permitted to identify high eccentric retrograde orbits as strongly indicators of their belonging to the halo population (Pauli et al. 2006 ). Although the number of halo members was sparse, an estimate of the age of the inner halo has been possible ( Gyr; Kalirai 2012 ). A key ingredient of these studies is the white dwarf luminosity function. Defined as the number of white dwarfs per bolometric magnitude unit and cubic parsec, the white dwarf luminosity function is a valuable tool to derive the age, history, and evolution of the components of our Galaxy. Moreover, the luminosity function holds all the information about the cooling process of the white dwarfs, being then an excellent tool for testing the physics of evolutionary models (see García-Berro Oswalt 2016 , for a comprehensive review about these issues). However, the effectiveness of the white dwarf luminosity function requires the existence of a complete, well-defined volume sample. In this sense, the lack of accurate distances previous to the Gaia era, joint to the selection biases inherited from magnitude-limited samples, have hampered the achievement of more conclusive results in such an elusive sample as the halo white dwarf population. The first observational halo white dwarf luminosity function (Liebert et al. 1989 ) contained only five objects, and no more than 20 were proposed as halo candidates through a neural network artificial intelligent classification algorithm (Torres, García-Berro Isern 1998 ). Based on the SuperCOSMOS Sky Survey observations towards the southern