The Asp Explorer is the best exploration ship. The only one that can jump further and have more equipment is the Anaconda, with an outfitting worth several hundred millions.
The Asp's jumprange is in the same ballpark as the DBX, but is has more internals to equip repair kits or whatever you want to bring with you, and more importantly you can equip a bigger fuel scoop. With the best fuel scoop, you can refuel entirely in 36 seconds, compared to 1min33s in the DBX, which makes a tremendous dfference when you have to refuel all the time during an exploration trip.