The question has been floating around for decades, but is still very pertinent. Can you fulfill the mitzvah of tzitzit on a mesh garment.

I came across three good online sources, so that should probably be your first stop:

Din Online - Mesh Tallit Katan - Concise and clear, a good place to start
Mi Yodeya - If I wear a synthetic and/or mesh garment with Tzitzis, will I fulfill the mitzvah of Tzitzis?
Yeshiva Har Bracha - Tzitzit on a Synthetic Garment - scroll down to the section headed, "Synthetic Tzitzit Distributed in the Army"

In the Yeshiva Har Bracha article, Rabbi Melamed concludes with an argument that today's synthetic garments are vastly superior to those made a few decades ago, and they are now much more commonplace; rather than a fringe textile (no pun intended) they account for 70% of all garments manufactured worldwide. 

In the Mi Yodaya piece, I see that I left a comment some thirteen years ago, suggesting that since the mesh doesn't really cover you, perhaps it cannot be considered a wearable garment. However, in retrospect, I think the piece of Gemara that came to mind discusses whether a given garment is viable only in terms of the size factor.

By the way, just yesterday we received a shipment of mesh tzitzit from a new supplier that makes them with softer material and much smaller holes.