Completeness of data on isogeny classes of abelian varieties over finite fields (reviewed)

For each dimension $g$ and field $\mathbb{F}_q$ with a nonempty collection of isogeny classes in the database, the collection of isogeny classes is complete. As of October 2020, the data was complete for the following pairs $(g, q)$, where $q$ ranges over all primes and powers of a prime in the interval:

• for $g = 1$, data is available for all $2 \leq q \leq 499$ and $q \in \{512, 625, 729, 1024\}$,
• for $g = 2$, data is available for all $2 \leq q \leq 211$ and $q \in \{243, 256, 343, 512, 625, 729, 1024\}$,
• for $g = 3$, data is available for all $2 \leq q \leq 25$,
• for $g = 4$, data is available for $q = 2, 3, 4$ and $5$,
• for $g = 5$, data is available for $q = 2$ and $q=3$
• and for $g = 6$, only $q=2$ is available.

Here are some further comments on the extent of the data.