far as i knew, currently, all 3ds game cards can just work on N3DS V4.1-4.5,now that your console has been updated to v7.1.0-16,i'm afraid,there havnt any cards can support running 3ds games on this latest 3ds version. All you can do is buying a flash kit play nds games or gba games. If r4i card is your favorite, then suggested you buy this card : http://www.modchipfactory.com/wood-r4i-...s-lite-p-1.html ,this is the best r4 card,uses famous wood firmware,with a regular updating and top game compatibility.
Sorry for all 3ds game cards can just run 3ds games on N3DS V4.5-4.1. if you really want to play 3ds games, you have to borrow one or buy a new one. As to the 3ds flashcart, recommend you the MT card. MT Card is one of the best 3Ds flash carts till now,Support Multi 3DS Roms; Support NAND-emulate;with the newest firmware v1.2 , support pokemon xy, Eshop.
All of the working 3ds flah cards so far only work on 4.1-4.5, currently nobody has been able to get 3DS flashcarts to work on 3DS firmware beyond 4.5. Since you have updated your 3ds to the latest 7.1.0-16, I'd recommend this r4i gold 3ds rts card, http://www.r4flashcart.com/8-wood-r4i-g...nd-ds-lite.html it allows to play almost all ds backups on your 3ds
