starburst detected in the 3$<$z$<$4 bin. We thus do not analyze this bin, because of its lack of statistical significance. The other bins contain 3, 6, 6, and 8 strong starbursts, respectively, by increasing redshift.\
The sample of main-sequence galaxies is contaminated by the starbursts which have sSFR$<$10 sSFR$_{\rm MS}$ . We expect that this contamination is negligible, since the contribution of all starbursts to the infrared luminosity density is lower than 15% [@Rodighiero2011; @Sargent2012]. To check this hypothesis, we statistically corrected for the contribution of the remaining starbursts with sSFR$<$10 sSFR$_{\rm MS}$ based on the @Bethermin2012b counts model. We assumed both the SED library used for the model and the average SED of strong starbursts found in this study. We found that this statistical subtraction only affected our measurements at most at the 0.2$\sigma$ level. Consequently, we have neglected this contamination in the rest of our study.\

[ccccccccc]{} Redshift & S$_{24}$ & S$_{100}$ & S$_{160}$ & S$_{250}$ & S$_{350}$ & S$_{500}$ & S$_{850}$ & S$_{1100}$\
& $\mu$Jy & mJy& mJy& mJy& mJy& mJy& mJy & mJy\
\
0.25$<$z$<$0.50 & 410$\pm$23 & 11.87$\pm$0.76 & 23.30$\pm$1.49 & 12.54$\pm$0.97 & 6.43$\pm$0.53 & 2.64$\pm$0.32 & -0.18$\pm$0.23 & 0.21$\pm$0.08\
0.50$<$z$<$0.75 & 247$\pm$13 & 6.37$\pm$0.43 