Computer people like powers of two. Nature generally does not.
The ratio between adjacent fields as you go from dorsal to ventral follows a somewhat different distribution - more of a logarithmic spacing. A commonly measured value is 1.14 (square root of 2) See if this helps:
Buried in this is an amazing gem - " This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned."
Connecting multiple spatial scales to decode the population activity of grid cells (Martin Stemmler, Alexander Mathis, and Andreas V. M. Herz)
A principle of economy predicts the functional architecture of grid cells (Xue-Xin Wei, Jason Prentice and Vijay Balasubramanian)
ROBUST AND EFFICIENT CODING WITH GRID CELLS (LAJOSVÁGÓ AND BALÁZS BUJFALUSSY)
What I don’t see in these papers is consideration of how this might be working in other parts of the brain. The WHERE stream is well represented but what about the WHAT stream? What do the patterns there mean and how are the two streams connected?