Ive mentioned this before on here a few times, so will repost what I have said then;
I grow carrots in 12 inch width by 9 inch height pots I grow mine as baby carrots.
I grow Amsterdam Forcing, Chanteray and Touchon and have done for over a decade.
I sow over a few months from Feb to June and pick through the harvesting season, June to October and for Touchon, September to January.
I sow thinly, but do thin out seedlings and pop them in spare pots.
Do cover them with netting for their early growing stage, more to prevent animals digging up the bare soil than carrot fly (that Ive never seen here).
I like pots as I have them placed all around the plot.