I would say it's your soil. If the soil is to compact the carrots won't grow properly. Where is the soil from? It may also be lacking in nutrients.

Here is a link that might be useful: Urban Farm Wife

Compact soil is probably not the problem, if it was just put in and was still loose. But it could lack nutrients -- did you mix in compost?

I'd guess it was the amount of sun -- between the site and the weather. Counting days from seedling emergence sounds like a good idea; it took my carrots a month or more just to sprout, because of the cold.

The 70 days on the package is just an estimate, probably based on weather and sunlight conditions more ideal than yours. You're better off to pull up one or two carrots and, if they're tiny, wait a while longer. I'd guess that if you'd waited another month, you'd have gotten full-size carrots.

You really have to take those packet days to maturity with a grain of salt. It's a guideline only and really only useful to compare maturation times with other varieties. The reality in the garden is that sooo many things affect days to maturation that there's no way a seed packet could cover every situation.

I also doubt it was your soil. We have a very heavy, silty soil here that acts much like clay - super heavy, crusts easily, drains poorly - and we grow carrots with no trouble at all. Carrots are low-demand, root vegetables, so unless you were dealing with severely terrible soil, nutrition shouldn't have been an issue either (especially since clay tends to hold on to nutrients).

Carrots are really slow to germinate when the conditions are anything less than ideal. If it's too dry/wet/cold/crusty, they just sit and wait... and wait and wait and wait.

They also need to be weeded diligently. If you were lax in the weeding department, that will have delayed them as well. I've gotten behind myself this year and you can distinctly tell which carrots in my rows had thistle competition and which did not.

Four or five hours of sun a day probably isn't enough for quick growth either, though I'm sure they would get there eventually.

Except for the weeding, I really don't think you did anything particularly wrong except not wait long enough. The variety you chose looks like it would have pushed through clay nicely (unlike an imperator type, for example). I'd almost bet money that if you'd left them alone for another month or two, you'd have had some nice carrots there.

If you're interested in some sort of reference, I grow varieties of nantes carrots that range from 55 to 75 days to maturity, according to the packet. I plant mid to late May and dig up the main harvest (for winter storage) usually mid to late September, depending on when our first frosts show up. That's roughly four months (at least) from seeding to harvest, regardless of the variety.

As Nygardener mentioned, the days to maturity on seed packets is just an estimate, and that estimate is further complicated by meaning either from seed germination for things normally direct sown (such as carrots, squash, etc) or from date of transplant (such as tomatoes, eggplants, peppers, etc). I use the DTM listing as a guide to figure early, mid and late season varieties for different varieties within that type of plant, because the actual production of harvestable size is totally dependent on the actual growing conditions. I don't think I've ever had a plant produce exactly on schedule, but usually the ones listed as being relief within their group are a bit earlier than the ones listed as later. It's just nature being nature, nothing that you're doing wrong.

I found this article to be of great help when I was learning to grow carrots. For me, the challenges were getting my clay soil truly loose to about a fourteen inch depth, and getting the Ph right. I had some beauties this past winter. I planted them in the fall, October, I think, and harvested most of them in March. The cold weather of winter keeps them growing very slowly...way longer than the packet said.

Here is a link that might be useful: How to grow carrots