what dot tire for 15x3 rim

Street tire hence the d.o.t.,dont want some short profile tire scraping the oil pan.The taller the tire the longer the roll out on the beams if I do race it.

you don't want to do much normal road driving on that narrow of a tire, you run the risk of rolling it right off the rim and it will understeer like a bast%$d

why not have a set of tires for the track and one for the street, only takes what 15 minutes to switch all 4 tires if there already on a set of rims