16x16x16 = 4096 = 2^12 = 12 bits = 1.5 bytes
32x32x32 = 32768 = 2^15 = 15 bits = a bit short of 2 bytes
Doubling each dimension of the system will always increase the size of the minimum binary number needed to address each sector by 3 bits.
While that's a fun fact, those values really don't have any direct correlation to how sectors or systems may be represented in Starmade's source code. Schema could be storing collections of data structures containing system data, in which case addressing a given sector is a 4 or 8 byte pointer, depending whether you have a 32- or 64-bit executable. Or, he could be bit-masking a char or byte value and using the result to directly access a hand-allocated sector array in memory.
The code could be very flexibly designed, with sector size determined by variables or modifiable constants, and a generic algorithm used to load sectors and populate the galaxy map. Or there could be a low-abstraction, high performance algorithm that takes advantage of the power-of-2 design decision for sectors and systems to save computations, but is specialized for systems exactly 16 sectors on a side. It could also be something entirely different. We can't know how easy it would be to change sector size unless Schine tells us, or we can sneak a peek at their code.
You got me curious, though.
What got you wondering about different system sizes? Is it something that would change gameplay?