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Jun 9, 2022 at 21:32 comment added Christophe Leuridan @Ilya Bogdanoiv. You are right. Giving a too simple answer can be a way to get more precisions on the nature of the bound wished (is it wanted for $\ell/m$ close to $0$, close to $1/2$, close to $1$ ?). Anyway, I completed my answer to give a less trivial bound when $\ell \ge m/2$.
Jun 9, 2022 at 21:23 history edited Christophe Leuridan CC BY-SA 4.0
I completed the answer.
Jun 9, 2022 at 8:48 comment added Ilya Bogdanov The bound you put is trivial after looking at the question. I assume the OP asks for more interesting ones...
Jun 9, 2022 at 8:30 history answered Christophe Leuridan CC BY-SA 4.0