The most important thing is to not fertilise the soil immediately before growing carrots. They are best sown into soil or potting mix that was fertilised for a previous crop - ie up to 6 or 9 months previously. Too rich a growing medium will cause carrots to grow stumpy or forked. One of the reasons is because the roots (carrots) don't have to grow down deep in search of nutrients.
Market gardeners tend to grow carrots and other root veggies in light sandy loam that offers little resistance and which hasn't been fertilised since before the previous crop.
You need a minimum depth of soil/potting mix of around 300mm for carrots - in fact for all veggies. Any shallower than this and there's not enough depth for roots to grow down and securely anchor plants. Over summer, shallow soils also tend to become quite hot and will dry out very quickly. My preference is for soil depth between 450 and 600mm.
Remember to practice crop rotation too, even in a raised bed. Don't grow the same crop in the same spot year on year. - Noelle
For my root veggies, I sieve my garden soil mix through a homemade mesh frame so the soil is loose and also free from hard clumps that may get in the way of a newly formed vegetable or roots. I also make sure there is depth to the soil, so carrots can grow down and potatoes can grow up.
This will sound silly, but I actually measured a carrot from a store, which I considered a 'normal' size and a bit of wishful thinking for my growing. Then when planning the bed and considering a pot, I made sure I cleared that measurement by maybe 5 or 6 inches so excess moisture would drain lower down and away from the veg.
I've had good results so far, so I just stick to this method. That and feeding them at planting and during growing of course. This is all just my own guess work and what has worked so far and not based on any guides. - rattle
I grow my carrots in a plastic raised garden bed from Bunnings (only $29.95 and about 90 X 40 cm). Carrots like to germinate in the dark so I sow fairly thickly, cover with the finest layer of seed starting mix, water with a mist and then cover with damp cardboard.
You need to check the seeds daily for sprouting after about 7 days. The moment you see sprouts emerging, remove the cardboard. Keep them moist as they grow and when they are up to it deep water them often.
I use a sifted premium potting mix with a bit of perlite and some organic slow release fertiliser added to it. The fertiliser has a bit more phosphorous in it to encourage root formation. - pjturner2008