We have carried out an extremely long integration-time (9000 s/beam) 21-cm blind survey of 60 square degrees in Centaurus using the Parkes multibeam system. We find that the noise continues to fall as sqrt(t) throughout, enabling us to reach an HI column-density limit of 4.2 x 10^18 cm^-2 for galaxies with a velocity width of 200 km/s in the central 32 square degree region, making this the deepest survey to date in terms of column density sensitivity. The HI data are complemented by very deep optical observations from digital stacking of multi-exposure UK Schmidt Telescope R-band films, which reach an isophotal level of 26.5 R mag arcsec^-2 (~27.5 B mag arcsec^-2). 173 HI sources have been found, 96 of which have been uniquely identified with optical counterparts in the overlap area. There is not a single source without an optical counterpart. Although we have not measured the column-densities directly, we have inferred them from the optical sizes of their counterparts. All appear to have a column-density of N_HI = 10^(20.65 +/- 0.38). This is at least an order of magnitude above our sensitivity limit, with a scatter only marginally larger than the errors on N_HI. This needs explaining. If confirmed it means that HI surveys will only find low surface brightness (LSB) galaxies with high M_HI/L_B. Gas-rich LSB galaxies with lower HI mass to light ratios do not exist. The paucity of low column-density galaxies also implies that no significant population will be missed by the all-sky HI surveys being carried out at Parkes and Jodrell Bank.
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