Typical carrot varieties have over 9000 seeds per ounce. 2x9000 = 18, 000 seeds.
The only thing I find surprising about 4000 carrots from over 18,000 seeds is that you didn't get far more. That is only about 20% if my math is good which is a very low % in my experience...but I could be wrong. No offence intended but it doesn't sound like a good idea to me.
p.s. on the board method I see about 80% germination rate. Just for fun I asked AI what the typical germination rate for carrots is:
"Under standard direct‑sow conditions,
carrot seeds germinate at about 40–60%. With improved moisture control via boards, rates commonly rise to
70–85%, and controlled tests have shown
up to 89% germination."