of the imaging data at longer wavelength in our analysis. As mentioned above, we select the $i' \leq 26.0$ LBGs, and we use the Subaru/*i’*, *z’*, updated-*z’*, UKIRT/*J*, and HST/F125W band filters for the $\beta$ measurement. Under the condition, for instance, the galaxies with $i' = 26.0$ and $\beta < -2.0$ have the larger photometric uncertainty in the *z’*, updated-*z’*, *J*, and F125W band filters compared with the galaxies with $i' = 26.0$ and $\beta \geq -2.0$, and hence the bluer galaxies have the larger uncertainty in $\beta$. Moreover, the sample completeness of the extremely blue galaxies such as $\beta \sim -3.0$ is also influenced by the depth of the imaging data although the extremely blue objects are rare. From equation \[eq1\], the case of $\beta = -2.0$ is derived from $M(\lambda_{x}) = Const$, namely, all the broad-band photometry is same. For the appropriate $\beta$ measurement with the wide $\beta$ range, it is required that the magnitude threshold of *i’* band is brighter than the $\sim$2–3$\sigma$ limiting magnitude of the *z’*, updated-*z’*, *J*, and F125W bands. Our selection criteria described in section \[S2s2ss\] is applied by taking the aspect into consideration. We use the conservative criteria and consider that our 