"Required rigidity" is quite subjective. Certainly this design is well tested around here and provides "enough rigidity". You have two options at this point; copy something that works, or do all the maths and arrive at your own answer based on what you want to cut and your machine design.

There's a mechanical deflection spreadsheet around here somewhere, probably in the gantry design threads. You can use that to see how different dimensions on the L will affect the maximum deflection given a standard set of conditions like gantry span and weight of the Z axis. Because your width is smaller than mine if you used the same profile you'd get less deflection for the same Z weight.

I suggest you go and have a play with the spreadsheet to discover the relationships. Ultimately it depends on what tolerances you're happy with.