We have analysed 18 ALMA continuum maps in Bands 6 and 7 , with rms down to 7.8 \mu Jy , to derive differential number counts down to 60 \mu Jy and 100 \mu Jy at \lambda = 1.3 mm and \lambda = 1.1 mm , respectively .
Furthermore , the non-detection of faint sources in the deepest ALMA field enabled us to set tight upper limits on the number counts down to 30 \mu Jy .
This is a factor of four deeper than the currently most stringent upper limit .
The area covered by the combined fields is 9.5 \times 10 ^ { -4 } ~ { } deg ^ { 2 } at 1.1 mm and 6.6 \times 10 ^ { -4 } ~ { } deg ^ { 2 } at 1.3mm .
With respect to previous works , we improved the source extraction method by requiring that the dimension of the detected sources be consistent with the beam size .
This method enabled us to remove spurious detections that have plagued the purity of the catalogues in previous studies .
We detected 50 faint sources ( at fluxes < 1 mJy ) with signal-to-noise ( S/N ) > 3.5 down to 60 \mu Jy , hence improving the statistics by a factor of four relative to previous studies .
The inferred differential number counts are dN / d ( Log _ { 10 } S ) = 1 \times 10 ^ { 5 } ~ { } deg ^ { 2 } at a 1.1 mm flux S _ { \lambda = 1.1 ~ { } mm } = 130 ~ { } \mu Jy , and dN / d ( Log _ { 10 } S ) = 1.1 \times 10 ^ { 5 } ~ { } deg ^ { 2 } at a 1.3 mm flux S _ { \lambda = 1.3 ~ { } mm } = 60 ~ { } \mu Jy .
At the faintest flux limits probed by our data , i.e .
30 \mu Jy and 40 \mu Jy , we obtain upper limits on the differential number counts of dN / d ( Log _ { 10 } S ) < 7 \times 10 ^ { 5 } ~ { } deg ^ { 2 } and dN / d ( Log _ { 10 } S ) < 3 \times 10 ^ { 5 } ~ { } deg ^ { 2 } , respectively .
Determining the fraction of cosmic infrared background ( CIB ) resolved by the ALMA observations was hampered by the large uncertainties plaguing the CIB measurements ( a factor of four in flux ) .
However , our results provide a new lower limit to CIB intensity of 17.2 { Jy deg ^ { -2 } } at 1.1 mm and of 12.9 { Jy deg ^ { -2 } } at 1.3 mm .
Moreover , the flattening of the integrated number counts at faint fluxes strongly suggests that we are probably close to the CIB intensity .
Our data imply that galaxies with star formation rate ( SFR ) < 40 ~ { } M _ { \odot } / yr certainly contribute less than 50 % to the CIB ( and probably a much lower percentage ) while more than 50 % of the CIB must be produced by galaxies with SFR > 40 ~ { } M _ { \odot } / yr .
The differential number counts are in nice agreement with recent semi-analytical models of galaxy formation even as low as our faint fluxes .
Consequently , this supports the galaxy evolutionary scenarios and assumptions made in these models .