full list of our $z=$ 7–8 sample is tabulated in Table \[tab:target\].

MOSFIRE Y-band Observation {#sec:obs}
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Observations were taken with MOSFIRE on the Keck I telescope over 4 nights during January 11 and January 13–15, 2015. We used the $Y$-band filter, to search for Ly$\alpha$ emission at $7.0 < z < 8.2$, with a 07 slit width correpsonding to a spectral resolution of $\sim$3 Å ($R=3500$). Most of the data were taken with 180 s exposures per frame, except that for the data taken on one night (January 15; for a total of 0.9 hr integration time) 60 s exposures per frame were used. We adopted an ABBA dither pattern with an $\pm$ 125 offset along the slit for sky subtraction. The seeing measured from the star placed on a slit was in the range of 06–09, with a median/mean of 07. In total, we obtained a total on-source integration time of $\sim$10 hr (from 2.8 hr (January 11) + 3.2 hr (January 13) + 3.2 hr (January 14) + 0.9 hr (January 15)), among which $\sim$7.3 hr was obtained in good conditions. These observations are among the deepest observations ever taken for $z \gtrsim 7$ galaxies.

Data Reduction
