Questiona6400 + Sigma 18-50 for my daughter's gymnastics, need a different lens?

My daughter started competitive gymnastics and the gym lighting is pretty bad. I have an a6400 with the Sigma 18-50 2.8. Pictures are either blurry or really grainy. We sit in the stands so I'm maybe 30-50 feet away. Do I need a longer, faster lens? Budget is a few hundred dollars. Thanks in advance. She's on beam and floor mostly, and they don't allow flash. I'm shooting in auto right now, which I'm guessing is half the problem.

Distance is the problem more than the lens. At 50mm from the stands you will crop a lot, and cropping shows the noise much more. For this the Sigma 56mm f/1.4 is the usual cheap answer on APS-C Sony, it is small, sharp wide open, and about two stops brighter than your zoom at the long end. A used 85 1.8 is also good if they let you stand closer.

Settings: shutter 1/500 minimum for gymnastics, 1/1000 for the bars and the vault. Aperture wide open. ISO auto, and let it go where it needs, even 6400 or 12800 on the a6400. Continuous AF with tracking.

Then denoise in software afterwards, it works very well now. A noisy sharp photo you can clean. A blurry photo you cannot fix.

Also sit at the end of the stands nearest the beam or floor, not in the middle. Fewer heads in the frame.

grainy and sharp beats clean and blurry every single time. don't be scared of high ISO on the a6400, it's better than you think, and the denoise in lightroom these days is properly good. i shoot my nephew's netball at 6400 and nobody's ever complained

Thanks both! Ordered a used Sigma 56 and I'll try 1/500 at the meet on Saturday. Appreciate it.