Increase the display quality 3D plot tick marks and labels

Question

I can get crisp, anti-aliased 2D plots but not 3D.

Anti-aliasing is set to 1 in Graphics options. In the Documentation center, 3D plots look good when I open it, especially the ticks and tick labels but when I recompile the plots, they lose their quality. I tried various RenderingOptions but none seem to work. My output of inxi -G is

Graphics:  Device-1: Intel UHD Graphics 620 driver: i915 v: kernel 
           Display: x11 server: X.Org 1.20.8 driver: intel unloaded: modesetting resolution: 1920x1080~60Hz 
           OpenGL: renderer: Mesa Intel UHD Graphics 620 (KBL GT2) v: 4.6 Mesa 20.1.3 

I am running Mathematica 12.1 on Manjaro KDE.

Edit:

David G. Stork's answer makes the surface of the 3D plot better but I would like to make the tick labels and tick marks crisp and smooth as in 2D plot if possible.

Answer 1

Just use a large number of plot points:

PlotPoints->100

And save as .eps or .pdf.

Answer 2

SetOptions[Plot3D, 
  BaseStyle -> {FontFamily -> "Times", FontSize -> 15}, 
  LabelStyle -> Directive[Black, Bold, Medium], 
  TicksStyle -> Directive[Small, Blue]];
Plot3D[Sin[x*y], {x, 0, 2 \[Pi]}, {y, 0, 2 \[Pi]}, PlotPoints -> 50, 
 AxesLabel -> {x, y, Sin[x*y]}]