pert:
How high?
What I found is you want to assemble as much as possible of your page at once and send it all at once rather than sending it in a bunch of small parts. I've been mostly using them standalone lately, rather than running AT firmware connected to a standard Arduino and there's a limit to how much you can send at a time, which I haven't found documented anywhere after a bunch of searching, I'm just sending it whenever it gets over 1000 characters long. I'm guessing it's the same with the AT firmware.Even with that it still seems slower to load than it should be. Using in AP mode doesn't seem to make a difference. Luckily I haven't used it for an application where speed is important yet.
I tried 230400 bps and it didn't seem to work.
I solved my very slow download time thus:
I have the web page in a file on the SD card and I was reading the html and sending it out a line at a time.
That meant character analysis to find the end of line markers (\n and \r) and it was primarily responsible for slowing it down.
On top of that I was looking for markers in two lines of html in which to insert a RTC battery voltage value, thus further slowing things down.
What I ended up doing was splitting my html file into two separate files with the bulk of the html in the first file and the last dozen or so lines (with the markers) in the second file.
The first file with most of the html and javascript is read 2000 bytes at a time and output 2000 bytes at a time to the wifi client.
Then only the second file is read one line at a time so that I can find the text markers and replace them with the battery voltage.
I managed to get the web page download time down from over 50s to about 13s