Ferrite rod antennas (loopsticks) present a design challenge because of size, weight, and cost.  One of the fundamental questions is long or fat?  These gents have the answer:

https://ietresearch.onlinelibrary.wiley.com/doi/full/10.1049/joe.2013.0126

They found, through mathematics that's way above me, that the optimum aspect ratio is 20.  That is, for a given diameter, the rod should be 20 times that long.