Sub-woofer fast enough for Horns?

What makes you think horns are 'faster' than anything else? Empirically horns would measure slower than any other type of speaker due to all the stored energy from reflections inside the throat.

My suspicion is that the Rel sub was just fine, it's the integration that needed work. Suboptimal placement will give the impression that the subs are too slow, the sound will appear to lag behind the impulse from your mains, when reality is small placement changes is all that's needed.

Bob_ +1 I must have at least eight subwoofers in cars, Bass amplification, computers, two channel, and HT. And I don't have a clue as to what is meant by slow sub?

I compared a REL Studio III with a JL Audio F113 and my DD-18 Velodyne in my two channel setup. To get the REL to integrate on its own it was a matter of lowering its gain to an unacceptable level. By comparison this sub with its high level connection method was a total joke but I can't say it was slow.

Using a line level connection from the Velodyne EQ to the REL helped a great deal. It also freed up the ability to find a better acoustical location. Connected to the REL my main speakers lost a bit of everything. But hey, they have a huge following.

I guess out of phase could give the sensation of slowness but most powered subs have a phase switch.

There can be a noticeable difference in presentation between small and large driver subs. Is that slowness?

Hi, The op asked about subs that are good for horn speakers, look no further than the JBL array subs!, they were built to use with the JBL top models, like the array line, everest line and K-2 lines, fast?, I would say so, cheers.

The OP has not even said what loudspeaker he is trying to match with a sub. There is not enough info to make an informed recommendation.