This question - sequel of PCB antenna: ground plane layers and dimensions?, talking about an IFA:
The only dimension that really matters is the length/width of the ground plane, or parallel to the spine of the F. This is the length of the edge forming our other half of the dipole. And the answer is pretty simple
As close to λ/4 wide as possible. This is always the distance of the L part of the F. So it will generally be slightly wider than the F's length spine-wise. If it is smaller, you will start losing bandwidth. If it is larger, you will get an increasingly multilobed radiation pattern. For a nice, omnidirectional pattern, quarter-wavelength width is best.
This sounds about right for electrical antennas, although, for an 'L' shaped antenna, shouldn't the ground plane better mirror it if it followed its 'L' contour?
How about magnetic antennas, i.e. single-point fed loop antennas, which use part of the ground plane to close the loop and form the H field within?