Id say at least 4" with something under for the the roots if your looking for the smallest cube for a specific reason. There is smaller but i would not recommend limiting your plant to such a small root zone.
If you care about the size id go with the 6"s.alot more room for the rootsand plant itself
Youll definitely need coco matts if your gona go the 4" route.
Or you could run rw slabs. Remember without a decent root base your plant will be limited
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I am planning a 49 plant per 1k grow using 4" blocks with rooted clones straight to 12/12. I have seen similar setups with 2 weeks veg in the blocks. No coco mat needed and results were very nice for a 7-8 week finisher with little to no veg.