We combined deep U-band imaging from the KPNO-4m/MOSAIC camera with very deep multi-waveband data from the optical to infrared, to select Lyman Break Galaxies (LBGs) at z~3 using U-V and V-R colors in the Subaru Deep Field. With the resulting sample of 5161 LBGs, we construct the UV luminosity function down to $M_{UV} = -18$ and find a steep faint-end slope of $alpha=-1.78 pm 0.05$. We analyze rest-frame UV-to-IR spectral energy distributions generated from the median optical photometry and photometry on median-stacked IR images. In the stacks of faint LBGs, we find a background depression centered on the galaxy. This deficit results from the systematic difficulty of SExtractor in finding faint galaxies in regions with higher-than-average surface densities of foreground galaxies. We corrected our stacked magnitudes for this. Best-fit stellar population templates for the stacked LBG SEDs indicate stellar masses and star-formation rates of log M*/Msun = 10 and 50 M$_odot$/yr at i = 24, down to log M*/Msun = 8 and = 3 M$_odot$/yr at i = 27. For the faint stacked LBGs there is a 1-mag excess over the expected stellar continuum in the K-band, which we attribute to redshifted [OIII]4959+5007 and H$beta$ lines. Their implied equivalent widths increase with decreasing mass, reaching $rm{EW_0([O III]4959,5007+Hbeta)}$ =1500A in the faintest bin. Such strong [OIII] emission is seen only in a miniscule fraction of the most extreme local emission-line galaxies, but it probably universal in the faint galaxies that reionized the universe. Finally, we analyze clustering by computing the angular correlation function and performing halo occupation distribution (HOD) analysis. We find a mean dark halo mass of log(Mhalo/h) Msun = 11.29$pm 0.12$ for the full sample of LBGs, and log(Mhalo/h) Msun = 11.49$pm 0.1$ for the brightest half.
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