This is related to problems of packing circles into an equilateral triangle, and covering an equilateral triangle by circles. Some data on these problems is available at http://www2.stetson.edu/~efriedma/cirintri/ and http://www2.stetson.edu/~efriedma/circovtri/

Since the Heilbronn triangle problem has been mentioned, that has data at http://www2.stetson.edu/~efriedma/heiltri/

This is related to problems of packing circles into an equilateral triangle, and covering an equilateral triangle by circles. Some data on these problems is available at https://erich-friedman.github.io/packing/cirintri/ and https://erich-friedman.github.io/packing/circovtri/

Since the Heilbronn triangle problem has been mentioned, that has data at https://erich-friedman.github.io/packing/heiltri/