Another cable sizing question

[ABerry82]

i have been asked to install a garage unit in a outbuilding they wanted a couple of sockets and lights and i think i allowed about 20A total output for design current. what size cable do you think bearing in mind its a 90 meter run in a trench from house to out building.i allowed 16mm does this sound like overkill

 

[Octopus]

And how do you propose to add it to the house CU?