In addition to what others have said, the most field you can
generate with the ferrite rod antenna will occur when it is
almost reaching saturation, and that takes a lot of ampere
turns. You can deliver more ampere turns to the rod than
your transmitter output can deliver if you resonate the coil
with a capacitor. That way, you have the current bouncing
back and forth through the capacitor added to the current
from the amplifier. If the coil-capacitor Q is, say, 100,
there will be 100 times more current through the coil than
the transmitter is delivering. This will probably take a
coil with a considerable mass of copper in it.

John, that is what I have seen! I resonated the antenna coil and driven it
with it's resonance frequency. Seems that the achievable distance was a
little more than the circuit without resonating capacitor.

You say, that driving the ferrite rod into saturation will force it to leave
more power into air? Why?

- Henry