Due to recent breakthroughs in 3DS reverse engineering there is now a way to unbrick your 3DS without a NAND backup.
Step 1: Brick your 3DS (or else you can't do this)
Step 2: create a new folder on your computer calles NAND
Step 3: fill it with files
Step 4: compress it and make sure it's the same size as a NAND dump. Must be zip file.
Step 5: rename it from NAND.zip to NAND.bin (make sure to change the extension)
Step 6: put NAND.bin on the root of your SD cars
Step 7: insert SD card into...
How to unbrick your 3DS without NAND backup
Step 1: Brick your 3DS (or else you can't do this)
Step 2: create a new folder on your computer calles NAND
Step 3: fill it with files
Step 4: compress it and make sure it's the same size as a NAND dump. Must be zip file.
Step 5: rename it from NAND.zip to NAND.bin (make sure to change the extension)
Step 6: put NAND.bin on the root of your SD cars
Step 7: insert SD card into...
How to unbrick your 3DS without NAND backup