The sketch is aggregated on a per-segment basis. However, if you're running multiple ingestion tasks each segment will generate its own segments.
I am not as familiar with Theta sketches as I am with HLL, but generally speaking sketches have a hire error rate when estimating very low cardinality counts. The HLL sketch has some mechanisms to mitigate this, where it will use a different method to calculate low cardinality then high cardinality. I do not know if Theta sketches have a similar mechanism.
My follow-up questions therefore are:
1. Is there a reason that you're using Theta vs HLL? Theta does support set operations that HLL does not, but for a simple count distinct HLL tends to be more efficient.
2. Is the 100 items a test case or realistic? If it is realistic, using an exact count distinct will probably perform better.