How can I build a fence that will keep rabbits out?

Consider installing snake fencing. A friend of mine did this under her deck.

We put on lattice backed with chicken wire.

you need to dig down into ground and place the wire(chicken wire cheapest to use ) then bury it so they cannot dig into ground and go under it at least 6-12"s down after all they are burrowing creatures;so using a 24-36" tall wire fencing would be best. 12" below ground level & 12"s above use either rebar or metal fence posts to install and make sure it's tight between posts. here's example of how it should look (video is kinda sad just look at fence install) https://www.youtube.com/watch?v=Rymv2tTB4R4 one more https://www.youtube.com/watch?v=_-Vog0KYK6A