All the kumihimo disks I have seen for sale have 32 slots. While it is easy to make smaller braids with smaller numbers of threads on these, it becomes harder as the number of threads increase.
It is possible to make a 32 thread hollow braid or a 32 thread kongo gumi braid on a 32 slot disk, but it can be tricky to remember where the groups start and end.
In the future, we plan to have some braids which will need several threads moved to make space for the ones in the middle, and this is virtually impossible to do properly if you do not have spare slots on your disk.
A number of people have made kumihimo disks from thick cardboard, or got foam (either thick, or several thinner sheets glued together) and made their own disks. The hardest part can be spacing the slots around the disk, so we have made some templates to help.
The commercial disks I have seen come in 95mm (3.8"), 107mm (4.25") and 150mm (6"). Each template file has a circle that will print out at each of these sizes with marks to show where to put the slots. You need to make sure the slots are long enough to hold the threads, but not so long that they are too weak and liable to break.