Context : Since the mid-1990s , the sample of Lyman break galaxies ( LBGs ) has been growing thanks to the increasing sensitivities in the optical and in near-infrared telescopes for objects at z > 2.5 .
However , the dust properties of the LBGs are poorly known because the samples are small and/or biased against far-infrared or sub-mm observations .

Aims : This work explores from a statistical point of view the far-infrared ( far-IR ) and sub-millimeter ( sub-mm ) properties of a large sample of LBGs at z \sim 3 that can not be individually detected from current far-infrared observations .

Methods : We select a sample of 22 , 000 LBGs at 2.5 < z < 3.5 in the COSMOS field using the dropout technique .
The large number of galaxies included in the sample allows us to split it in several bins as a function of UV luminosity ( L _ { \mathrm { FUV } } ) , UV continuum slope ( \beta _ { \mathrm { UV } } ) and stellar mass ( M _ { * } ) to better sample their variety .
We stack in PACS ( 100 and 160 \mu m ) images from PACS Evolution Probe survey ( PEP ) , SPIRE ( 250 , 350 and 500 \mu m ) images from the Herschel Multi-tied Extragalactic Survey ( HerMES ) programs and AzTEC ( 1.1 mm ) images from the Atacama Submillimetre Telescope Experiment ( ASTE ) .
Our stacking procedure corrects the biases induced by galaxy clustering and incompleteness of our input catalogue in dense regions .

Results : We obtain the full infrared spectral energy distributions ( SED ) of subsamples of LBGs and derive the mean IR luminosity as a function of L _ { \mathrm { FUV } } , \beta _ { \mathrm { UV } } and M _ { * } .
The average IRX ( or dust attenuation ) is roughly constant over the L _ { \mathrm { FUV } } range , with a mean of 7.9 ( 1.8 mag ) .
However , it is correlated with \beta _ { \mathrm { UV } } , A _ { FUV } = ( 3.15 \pm 0.12 ) + ( 1.47 \pm 0.14 ) ~ { } \beta _ { \mathrm { UV } } , and stellar mass , \log \left ( IRX \right ) = ( 0.84 \pm 0.11 ) \log \left ( M _ { * } / 10 ^ { 10.35 } \right ) +1.17 \pm 0 % .05 .
We investigate using a statistically-controlled stacking analysis as a function of ( M _ { * } , \beta _ { \mathrm { UV } } ) the dispersion of the IRX- \beta _ { \mathrm { UV } } and IRX- M _ { * } plane .
On the one hand , the dust attenuation shows a departure by up to 2.8 mag above the mean IRX- \beta _ { \mathrm { UV } } relation , when \log ( M _ { * } [ M _ { \sun } ] ) increases from 9.75 to 11.5 in the same \beta _ { \mathrm { UV } } bin .
That strongly suggests that M _ { * } plays an important role in shaping the IRX- \beta _ { \mathrm { UV } } plane .
On the other hand , the IRX- M _ { * } plane is less dispersed for variation in the \beta _ { \mathrm { UV } } .
However , the dust attenuation shows a departure by up to 1.3 mag above the mean IRX- M _ { * } relation , when \beta _ { \mathrm { UV } } increases from -1.7 to 0.5 in the same M _ { * } bin .
The low stellar mass LBGs ( \log ( M _ { * } [ M _ { \sun } ] ) < 10.5 ) and red \beta _ { \mathrm { UV } } ( \beta _ { \mathrm { UV } } > -0.7 ) , 15 % of the total sample , present a large dust attenuation than the mean IRX- M _ { * } , but they still are in agreement with the mean IRX- \beta _ { \mathrm { UV } } relation .
We suggest that we have to combine both , IRX- \beta _ { \mathrm { UV } } and IRX- M _ { * } , relations to obtain the best estimation of the dust attenuation from the UV and NIR properties of the galaxies ( L _ { \mathrm { FUV } } , \beta _ { \mathrm { UV } } , M _ { * } ) .
Our results enable us to study the average relation between star-formation rate ( SFR ) and stellar mass , and we show that our LBG sample lies on the main sequence of star formation at z \sim 3 .
we demonstrate that the SFR is underestimate for LBGs with high stellar mass , but it give a good estimation for LBGs with lower stellar mass , when we calculate the SFR by correcting the L _ { \mathrm { FUV } } using the IRX- \beta _ { \mathrm { UV } } relation .

Conclusions :