How many colors can L*a*b* describe?

Question

OK. So this is what was keeping me up at 3am this morning
RGB numbers can describe over 16 million colors in a 24 bit file. But looking at the L*a*b* numbers in Photoshop, that space can only describe just over 6.5 million colors. (L* has 0-100, a* and b* allow -128 to 127)
And LAB supposedly includes all colors, right? Colors outside of a typical RGB editing space. So that would mean even fewer colors to define an RGB space.
So, wouldnt that lead to problems when converting to LAB, or when Photoshop uses LAB as a Profile Connection Space?

Answer 1

Photoshop uses L*=0..100, a*=-128 to +128, b*=-128 to +128
(not -128 to +127). L* is coded in a TIFF by 0 to 255.
Meanwhile I've tested by a brute force counting the number
of available colors in Lab for three RGB spaces:
Define RGB space
N=0
For L*=0 To 100 Step 1 Do
For a*=-128 To +128 Step 1 Do
For b*=-128 To +128 Step 1 Do
Begin
Convert L*,a*,b* to R,G,B
If R,G,B in [0,255] Then N=N+1
End
Print N
The result, number of colors in Lab:
0.832.752 sRGB % almost one million
1.208.912 AdobeRGB(1998) % more than one million
2.659.728 ProPhotoRGB % almost three millions
In simple words: scan Lab by steps 1 and increment
the counter if the resulting RGB values are in the
allowed range 0..255.
Actually, the stepsize was 2 and the total result
was multiplied by 8.
Some more information is here in chapter 18:
http://www.fho-emden.de/~hoffmann/cielab03022003.pdf
Many conversions between RGB and CieLab, both for
8 bits per channel, back and forth, don't do much harm
(they are not 'destructive'), as shown, proved or
pretended by Dan Margulis, author of 'Photoshop Lab'.
I'm sharing his opinion, based on experience by much
practical image processing for offset printing.
Best regards --Gernot Hoffmann