Hmm pests!
Yes Lily, black netting is good, and UV treated so it lasts a long time.
A cage with 5mm mesh-size netting keeps out most moths & butterflies.
To go finer, you need white mesh, less attractive & more expensive.
I have not tried nematodes v carrot fly.
My experience with nematodes is that they are expensive, somewhat challenging to use (e.g. need to keep ground moist after application) and are probably not worth the cost/effort, though others like them!
Mesh against carrot flies is effective except in v bad years!