Question
From around 400 BCE to 1000 CE, what could what would a reasonable greatest achievable population be – under the best of all circumstances – in a rural area of about $\mathrm{900 km^2}$ (In which people may live in villages, but disregarding areas containing towns or cities with a population greater than 1000 people)
Edit: by best of all circumstances, I mean best of all circumstances achievable on an Earth-like planet, which includes the best climate for agriculture which could realistically exist.
Background
I am currently working on a strategy game set in a fictional -- but in all ways very Earth-like -- world in a period technologically -- including domesticated plants and animals -- comparable to the old world (Eurasia and Africa) from around the year 400 BCE to 1000 CE.
Data regarding the world is stored in a mesh, where each cell in this mesh stores information for an area with an area of close to $900\,\mathrm{km}^2$ (same as a $30\,\mathrm{km}$ by $30\,\mathrm{km}$ square but not necessarily a square).
One of these things which need storing is the rural population of the cells (towns and cities with a population greater than 1000 [a somewhat arbitrary limit] are by the game engine stored separately).
For performance and file size reasons, only 8 bit may be used to save the population of each cell; this 8-bit number will represent the population of the cell on a scale from 0 to 255 (the greatest 8-bit number) where 0 is a population of 0 and 255 is a population equal to the greatest population which might live in this area, and this is why I need to know this maximum population.
Further criteria
Note that I am not simply asking about the greatest population density of an entire iron age or medieval state or empire: consider for instance that the population density of a small rural area -- for instance near rivers like the Nile, the Tigris or Euphrates rivers -- may be much much greater than that of the states surrounding them.
For this reason, I do not consider my question to be answered by (and thus a duplicate of) this question: What is the difference of population density between the population of a nomadic and a sendentary territory?