Losing image quality during export in illustrator

I have a vector graphic in illustrator. I need the final png to be 200x200 px. I set my artboard to 200x200px and export it at 300 ppi and Anti aliasing Art Optimized. The final image is 730x797px.

The image is crisp but it's too big. If I export at 72 ppi I get the size I want but not the quality.

How can I have the same crisp image at 200x200px but with the same quality that I"m getting with the 300ppi?

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