Brush marks in finished work

[Jerry Lear]

I just finished a cherry platter, sanded to 420 grit, applied Danish oil & let dry. I then applied three coats of water based poly with a foam brush, letting each coat dry. After totally dry, I sanded from 500 to 6000 grit.
I noticed that there were brush marks in the finished product. I was careful not to go over the same areas.
Is there something I am doing wrong? Is there a way to eliminate or minimize these marks?
Thanks,

[Bob Bouis]

The sanding was supposed to get the brush strokes out. You didn't sand it enough.

[Bob Bouis]

Oh, if I can add to that. Maybe sand in between coats, or at least sand before the final coat. That'll help. Maybe thin the last coat a little too.

[Brian Kent]

I wipe on coats, whether oil-based or water based. Then I sand between coats with about 320 grit, until the base coats are smooth. After that I'll sand finer after every 1 or 2 coats. 500 to 6000 is plenty fine. I think the problem comes on earlier coats and grits.