The Coffin corner is the altitude at which a plane's stall speed is close to Mach 1, the speed of sound (but still below, at the critical Mach number). What accounts for a coffin corner at higher altitudes? I'd think of a larger wingspan, but on the other hand larger wings would make the plane heavier.
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The best you can do is to make the wing loading low. Wing aspect ratio helps, too, and if you look at existing designs, it will be similar to that of gliders and certainly higher than that of airliners or GA airplanes.
This answer covers the characteristics which make a high altitude possible and, besides wing loading, mentions the factor $\text{Mach}^2 \cdot c_L$. Poor designs only achieve a $\text{Mach}^2 \cdot c_L$ of 0.2 whereas good ones will reach 0.4.
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