Camera Lens Help. Once Again?

I'm still trying to find a good camera lens for shooting out doors lacrosse games that may be at night. I'm having trouble… I need a Nikon lens with a low f/stop and good zoom. Not as much zoom as the pro NFL photographers get! But just enough for me to get a good shot. Thanks.

Added (1). I would like a lens under $500 dollars… Is that possible if i want a low f/stop?

The 200-400 mm f/4 should be a great one.

The 70-200 mm may be too short.

The 28-300 mm may be too slow

I agree the 200-400 f/4 should be a great lens if you don't already have it.

Since we're not psychic, can you at least give us a hint of a budget? There are plenty of very good lenses out there, but some cost as much as a small car.

I'm sure you have discovered that fast aperture and telephoto in the same lens is not cheap. Nikon's own 70-200 f/2.8 VR runs $1, 800, and the new Version II is more like $2, 200.To make it even better, 200mm isn't really a long telephoto.

You can stay in the same range, 70-200 f/2.8 without stabilization, for $775 with the Tamron version, and $800 for Sigma. Tokina got out of the telephoto business, but still does some very good standard and wide lenses,

There are other long telephoto lenses that would be great for this, but not at night. Even an f/2.8 lens will be difficult to use unless the field is well lit and you can crank the ISO to 1600 or better. You gotta have light, no way around that.