  In this work, we investigate upper limits on the global escape fraction of
ionizing photons ($f_{\rm esc/global}^{\rm abs}$) from a sample of galaxies
probed for Lyman-continuum (LyC) emission characterized as non-LyC and LyC
leakers. We present a sample of 9 clean non-contaminated (by low redshift
interlopers, CCD problems and internal reflections of the instrument) galaxies
which do not show significant ($>$ $3\sigma$) LyC flux between 880\AA\
$<\lambda_{rest}<$ 910\AA. The 9 galaxy stacked spectrum reveals no significant
LyC flux with an upper limit of $f_{\rm esc}^{\rm abs} \leq 0.06$. In the next
step of our analysis, we join all estimates of $f_{\rm esc}^{\rm abs}$ upper
limits derived from different samples of $2\lesssim z < 6$ galaxies from the
literature reported in last $\sim$20 years and include the sample presented in
this work. We find the $f_{\rm esc}^{\rm abs}$ upper limit $\leq$ 0.084 for the
galaxies recognized as non-LyC leakers. After including all known detections
from literature $f_{\rm esc/global}^{\rm abs}$ upper limit $\leq$ 0.088 for all
galaxies examined for LyC flux. Furthermore, $f_{\rm esc}^{\rm abs}$ upper
limits for different groups of galaxies indicate that the strongest LyC
emitters could be galaxies classified as Lyman alpha emitters. We also discuss
the possible existence of a correlation among the observed flux density ratio
$(F_{\nu}^{LyC}/F_{\nu}^{UV})_{\rm obs}$ and Lyman alpha equivalent width
EW(Ly$\alpha)$, where we confirm the existence of moderately significant
correlation among galaxies classified as non-LyC leakers.
