[seqfan] Upper bound for A322348?

[Hugo Pfoertner]

Dear SeqFans,

Is there an upper bound for https://oeis.org/A322348 as a function of n?

An unanswered question in connection with the problem of convex grid
polygons of minimum area with a given number of boundary points is the
question of whether their diameter (or equivalently size of an enclosing
box) is bounded from above. See, e.g., A063984, A070911, or
https://oeis.org/A357888 .

The diameter is actually unlimited if one allows for shearing. However, if
one considers polygons whose diameter cannot be reduced by shearing, then
the question of the smallest diameter is essentially equivalent to the
question of an upper bound for A322348. The problem doesn't seem to be of
interest to anyone for more than 10 years and my similar question in
mathoverflow remained unanswered, apart from the reference to shearing:
https://mathoverflow.net/questions/433773/upper-bound-on-the-diameter-of-a-convex-lattice-n-gon-with-a-given-area

Does anyone know of any reported progress or has an idea how to at least
get to a rough upper bound? Nobody has any motivation to continue with the
numerical calculations for A070911, in which all programs described in
https://codegolf.stackexchange.com/questions/253633/the-smallest-area-of-a-convex-grid-polygon
deliver the same results, because there are no indications in which
direction the parameters of the search should be expanded.

Hugo Pfoertner