The largest sample of field galaxies to date is the Las Campanas Redshift Survey (LCRS; ref. 18), which has 1.9 × 104 galaxies. For -18 < MR < - 16 (approximately -16.5 < MB < - 14.5), the LCRS has a slope of = - 1.39 ± 0.11. The cluster slope over the same magnitude range is = - 1.44 ± 0.13.
There are, however, differences. Most of the faintest galaxies seen in the LCRS are emission-line galaxies where as most of the faintest galaxies in clusters are gas-poor dSph galaxies. Therefore, even though the LF slope is similar in the two environments for -18 < MR < - 16, the LF is dominated by the contributions from different types of galaxies in each.
Also, the field and cluster LFs are probably very different much fainter than MR = - 14. The steep turn-up seen in Virgo  for MR > - 14 certainly does not happen in the Local Group , for example. Although the Local Group may have several undiscovered low surface-brightness members at the very faintest magnitudes like MR ~ - 9 (the magnitude of Draco and Ursa Minor), it probably does not have many brighter than MR = - 12. Therefore incompleteness is not the reason for the discrepancy in the LFs here.