Version 1.3 of this hack is out now.
Changes in 1.2:

Now works on real DS! Albeit with slight issues, but they'll be fixed in a future release.
Simplified Bowser Shell and Chain Chomp models
Slightly improved music
New GCN Baby Park course
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Freezer on my Flash Card R4 Infinity ?

Version 1.4 released:

Updates to bottom screen maps
Music improvements
Course improvements
New menus
and more
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Version 1.5 is out now.
Changes from 1.4:

- Better music
- Better SFX
- Missions support (see the list)
- Course improvements
- MKDD karts have been removed and replaced by original MKDS karts with their corresponding beta models (except Toad Kart, which was used in the E3 2004 version as the standard kart)

Mission list:

1-7: Beta Mission 6
1-B: Beta Mission 9
2-5: Beta Mission 5
3-6: Beta Mission 2
4-3: Beta Mission 3 (Shroom Ridge has been edited to work with the unmodified beta mr03_tool.nkm)
5-1: Beta Mission 4
6-2: Beta Mission 7
6-6: Beta Mission 1
6-B: Beta Mission 10 (Chief Chilly)
7-3: Beta Mission 8 (uses the restored pre-beta model of Tick-Tock Clock)

All except Mission 8, use their original beta NKM. All other missions are either custom missions or the stock missions.
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Is it finally compatible with real hardware?

EDIT: nope............

How? You can post what's wrong, so I can take a look at to them.
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It just gives me a white screen, it does nothing else

Uh... this doesn't work on all flashcards, but works on some R4s, as reported by many who played this hack. I don't get why this happens, but you can try using NSMBe to extract all the files from the ROM (only the ones in the /data is recommended), and put them on a clean ROM.
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It worked just fine in my r4i 3d 2012 until i pressed Single Player and freeze on a black screen. It still didnt get ingame without crashing in any of my flashcard so i guess your hack is only playable in a very limited number of flashcards

I guess i will just use the emulator..

Version 1.6 is out, with improved sounds, and improved tracks, also the 28 unused missions restored:

tcrf.net/Mario_Kart_DS#Removed_Missions

Video:


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Version 1.7 is out now, with significant SFX and course quality improvements.

First post updated with the v1.7 link.
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Version 1.8 is now released, with updated graphics, models and SFX.
Also a lot of improvements up from 1.7.
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Version 1.9 is now released. This version includes new models for some courses (Desert Hills, GCN Yoshi Circuit, etc.) and also, quality improvements.
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Got it to work with my DSi
Secret Footage: https://www.youtube.com/watch?app=desktop&v=KNDRoRjt788&feature=youtu.be