This is what happens with the ultralight 3" concepts gets taken to a somewhat ridiculous extreme.

Originally the plan was to use this build to stress test the JHEMCU AIO boards and test out Betaflight 4.3 builds on this class of quads. Intead, I inadvertently created an absolute monster that can run down 5" quads using $8 batteries. The handling and agility on offer from this quad is insane, and for the actual cost of this build, it had me wondering if 5" quadcopters are really worth building for races.

Budget is still a significant consideration, and practically there are a couple change I will probably have to make with this as parts break, but overall I'm extremely happy with how this came out.

[[Update]] I did explode the frame on the second outing - I highly recommend running something different, the BetaFPV X-Knight3 is where I've been at.

Motors are the RCINPower 1207 5000KV motors. At the price Pyrodone had these, I just stacked them deep, and these are among the best motors that company has made for 3" applications (the older 1108's flew amazing, but were not very durable). These 1207's perform amazingly well, the realistic downside is that they don't cool terribly well, although some of this has to do with being able to burn down batteries in 80s on this setup.
Frame is a Pyrodone UL3 frame with TPU Pickle canopy (taken from a Diatone GTB-339). This combination is extremely lightweight overall, the overall stregth of the frame seems great for the weight, but I did break an arm on grass within the first 5 batteries, and none of the minor hits did enough to even knick or damage props, so I feel like the frame might be a weakpoint, or I got one that didn't quite cure right on the carbon composite. For similar cost, I'll probably move these electronics over to a BetaFPV X-Knight3 frame, since this has power to spare and a couple more grams of frame weight in exchange for durability should be worthwhile.
AIO Electronics was the initial basis of this build, and the JHEMCU 35A Gen2 AIO boards (F411 with Blackbox) really opens up some options, especially running 3S packs with some current overhead because this is a light build. The AIO is remarkably nice for a budget unit, and running JESC the setup parties (48kHz PWM, 0.25 Startup Power, MedHigh Timing, and Demag Comp on Low). The Betaflight 4.3 tune is straightforward, and I'm running it on DShot300 at 8k/4k Gyro/PID loops, as required for F411 chips. The actual tune is remarkably close to a 5" quad with RPM filtering running, but the lowpass filter can go way up comfortably because 3" stuff resonates at higher pitch. As always, an extra capacitor is worthwhile, in this case a 25V 220uF capacitor gave me all the overhead, especially if I want to run some 4S apcks.
FPV Gear is another budget set of choices... but ones I'd consider changing down the road Foxeer's Razer Nano is an excellent camera, period. I may swap it to a Predator because it flies well enough to deserve it, and the V4's are on closeout. The VTX is an PandRC $10 VTX, because it what I need it to. I feel as though this setup deserves a nicer PredatorNano and UnifyPro with Lollipop setup in order to achieve nicer video, but this actually works extremely well for racing.
Props are Gemfan, which are the best options on T-mount 3". The 3016's are quite excellent for overall grip and performance, but it's actually so much grip that I struggle to really make use of this at the limit, and actually prefer the Gemfan 3018 biblades on this particular setup. The taller 1207 stator can keep those props wound up in turns, and the straight line speed is pretty phenomenal. I feel like the biblades are kinder to the components, and the tune actually works extremely well on them. Finally, the sound is unique, and excellent with biblades being absolutely hammered to the limit, which is what this quad wants.
Batteries are the interesting part here. I can run 2S 450mAh/650mAh, 3S 450mAh/520mAh/550mAh/650mAH, and I've tried 4S 450mAh packs. On 2S, this feels like a more more planed GTB339, as the extra motor volume seems to cancel out the lower KV on performance, and the overall higher weight just helps ignore the wind.
On 3S packs the speed is monumentally quick, so much so that I can actually jump from my 6S 2250KV 5" race rigs to this and there isn't a big transition to readjust to speed, it's crazy. I do throttle limit slightly, because the 3S packs will hurt themselves supplying that much power, these motors can take all the power the battery makes, the that last 10% of throttle hurts the battery more than really adds thrust.
On 4S, I used a lot of throttle limiting, adjusted the PID tune, and still had some thermal issues -it does work, and I"m sure I could retune it, but those were expensive batteries, and the 3S 450mAh & 650mAH packs are so much cheaper and flew great out of the box, so those are my preference.

The speed from something this small is mind-bending.

I have a lot of other 3" quads that perform at astounding levels, but a lot of those feel like they're harnessing a particular prop and throwing motor (1408) at the problem until the speed gets there - this does it elegantly, and with the lower pitch props the delivery of power is exceptional. It sounds like the angriest sewing machine in history, and flies about how it sounds. It's comically fast, and cheap enough that I'll throw it into race heats with other pilot's 5" quads and accept that I might damage this flying into the back of other pilots... because that's how well it performs when I'm doing my part.