I made several Vrefs. The last one a LM399 and 0.01% low tempco precision resistors.
The biggest problem ( I think) at this moment is drift due to humidity changes. But it is only powered on for about a month so not burned in yet.
I'm monitoring this now every day 3 times, noting temp and humidity. The room temp is between 19 to 24 degrees and Hr is 30-35%. Biggest changes seems to be humidity.
The Vref (LM399 with a chopper LTC 1052 and a opa277) is now floating between 10.000,040 and 10.000,062 depending on temp and humidity. The next step will be ovenizing the whole Vref and adding battery power to suppress common mode problems. The 7.5 digit meter monitoring is also on 24/7 and modified by me to keep it inside at a steady 37 degrees.
Use good shielding, avoid thermal and mechanical stress, clean everything very good with IPA, never, and I mean never, do what Dave did in the video over his Voltstandard. Use your " dirty" fingers to grab the reference or opamps. ( when he pulled out the piggyboard, that was mounted like that for several good reasons. Removing it and replacing introduces mechanical stress, the greas an salt from your fingers degrade isolation resstanse with a factor upto 100. And then you got things like seebeck effect, triboelectrical effects ect. Keithley has a downloadable book on their site about measuring uV's that has a lot of good advise. Jim Williams wrote some good application notes on making Vrefs.
It takes several thousants of hours to get the best stability.
If you buy a 0.02% Vref you have a voltage somewhere between 4.999 or 5.001. That is not rather accurate. Good for a 2,5 digit meter. Add to that the resistors, if you use two 0.01% 10K and they turn out to be 9999 and 10001 ( murphy rules) you get an even bigger fault.
So to make a good reference you need a good meter to check it, and to check the meter you need a reference. Chicken and egg.