Finding the dimensions of waveguide filled with dielectric

My problem is:

Find the ranges of the dimensions a and b of a rectangular waveguide filled with dielectric e=2.56e0 with (u=u0) under the conditions that
-TE10 mode propagates with a 20 % safety factor (f=1.2fc)
-the frequency is at least 20% below the cutoff frequency of the next higher order mode, where f=3ghz
(where a is in the x direction and b is in the y direction)
My question is this

Since we are dealing with TE10 and TE20 modes (m=1,2 n=0,0)
does this mean that due to the fact that n=0 in both cases (npi/b) there is no restriction on the length of b as long as it is smaller than a?

Thanx

yws

"b" need not be smaller than "a". There is a class of waveguides called tallguides where "b" is amde large compared to "a". These types of guides are low loss guides.

You can check out http://tallguide.com