For now any treasure you would dig out belongs to the state, even something on your own property. Basicly what is under belongs to the state. Low remains unenforced most of the time but sometimes authorities would claim something offered for sale on ebay, allegro etc.
Some work is done to regulate it differently though - treasure hunters would get half of the value while the other half would be owned by the land owner.
In recent years there has been lots of people hunting and finding all kinds of things and media would sometimes inform on what was found and where if worthy their attention.