Doesn't Sigma make a 200-500 f/2.8 ... I think it weighs about 36lbs and costs $26,000.00. I heard Fox Sports used one to film and broadcast part of the World Series. So you could probably double or triple those figures to make one even faster.

Due to the optics involved, at a certain point it becomes impractical for normal use due to the size and weight of the glass elements. Look on Google for the Canon 5200mm f/14 prime lens.