I grow my carrots in a bottomless covered container about 15" deep,
which is filled with washed or sharpe sand.
Core holes out with a tube about 1" to 1.5" dia. (small bore plastic waste pipe) to bottom of the container.
Fill the holes with compost, which is a mixture of:
1 part fine peat moss
1 part sieved sterilised soil
1 part builders or silver sand
(each part = to a builders bucket)
To which is added:
4oz Vitax Q4 fertiliser
4oz garden lime
4oz fine calcified seaweed
Mix well together then fill holes to top making sure no air pockets are left. Leave a small depression in the top about half inch deep for about 4-5 seeds.
The varieties used this year are Trevor, Artemis & Maestro.
Cover seeds with a little more compost & water well. Then cover the surface with plastic to aid germination which is removed as soon as seedlings emerge
Allow to grow until big enough to thin out to 2 or 3 seedlings. Leave these to grow on to make small carrots before thinning to just 1.
Always keep container covered to guard against carrot fly & well watered.