what would be the smallest D and L for 556 that works at 140db?

I think you'd be asking a lot for anything under 1.5x6. Not saying there's a design out there that can't, but there'd have been a lot of effort put into its design. Enough so that it's proprietary info, perhaps.

Pretty much.  I've got a 1.56 x 5" model that comes in just under the threshold at 138.6, but that was done by making the entire thing of 17-4 PH with the base and baffle skirts forming the outer tube, much like the SiCo Omega, and also with a brake that's designed to maximize the blast chamber.  If you're talking about trying to buy 1.5" tube and use cones & spacers with direct thread mounting, I'd plan on at least 6" length.

Griffin's optimus micro is 1.1" in diameter and they exceed 140db. like mentioned 17-4 construction to handle the abuse. They also require extension modules to in essence make a larger blast chamber for some of their barrel length restrictions.

going smaller in diameter eats up internal volume in a hurry (pi r sq'd) so a longer can may be required to get your #'s. One way to cheat is to make a tubeless design. I'm not too sure how the weldability of 17-4 is (I want to say it was poor but I could be wrong) going tubeless yields more volume in a given size.

This is exactly what I did and 17-4 welds great.

Yup.  Fusion TIG welds beautifully, and even if you anneal the material in the HAF, you still have 150 KSI yield strength.  Few alloys have such high strength in annealed or normalized condition.

A 1.625 od x 5" titanum tube will meet your objective on a 16" barrel using a griffin armament minimalist taper brake and 4 rsc.