Export jpeg/gif for web without losing quality

[l_mfg]

I have to make a leaderboard (desktop and mobile). It has to be a jpeg or gif and max. 100kb (desktop) and 70kb (mobile) and 728x90px (desktop) 300x75px (mobile). 

So I use export for screens. But the quality is really not that good. Is there any way I can fix that?

This is a screenshot from my work in illustrator:

And this is the jpeg export:

[Ton Frederiks]

You can try PNG to get a better quality (and use Type Optimized).

The screenshot looks better because it is more than double the size of your jpeg export.

[l_mfg]

I know but I have to use jpeg or gif... so PNG is not an option.