Steel tube deflection over span
Given the length and aspect ratio that you've proposed, it will be very difficult to meaningfully support the desk the long way. 16' is just way too long to get any support across. Certainly a 2x4 will be basically useless, even "on edge". Also, consider the ergonomics of having a thick tabletop surface: if this is going to be a computer workstation area you do not want to have a very thick top since that will force people to sit too low and have their keyboard too high.

I suggest ignoring the ends and building the desk to be supported the short way, i.e. cantilevered out from the wall. If you look around you will find various floating / triangle desk bracket designs. You might also consider whether adding a few legs would really be a problem; that would make the desk substantially stronger (and/or easier to build).

Whatever you do, make sure the desk is sturdy. People will invariable pile a desk with books, computer equipment, etc. and even sit on &amp; lean against them.