The following pictures show n unit octagons packed inside the smallest known L (with short side s).
1. 
s = 1+3√2/4 = 2.06066+
Trivial.
2.-3. 
s = 1+√2 = 2.41421+
Trivial.
4. 
s = 3/2+5√2/4 = 3.26776+
Found by Jonathan Viquerat
in June 2026.
6. 
s = 3.55228+
Found by Jonathan Viquerat
in June 2026.
6. 
s = 3.88561+
Found by Jonathan Viquerat
in June 2026.
7. 
s = 2+3/√2 = 4.12132+
Found by Jonathan Viquerat
in June 2026.
8. 
s = 4.36459+
Found by Jonathan Viquerat
in June 2026.
9. 
s = 4.46274+
Found by Jonathan Viquerat
in June 2026.
10. 
s = 4.69035+
Found by Jonathan Viquerat
in June 2026.
11.-12. 
s = 2+2√2 = 4.82842+
Trivial.
13. 
s = 5.41620+
Found by Jonathan Viquerat
in June 2026.
14. 
s = 8/3+2√2 = 5.49509+
Found by Jonathan Viquerat
in June 2026.
15. 
s = 5.82397 +
Found by Jonathan Viquerat
in June 2026.
16. 
s = 5.93197+
Found by Jonathan Viquerat
in June 2026.
17. 
s = 6.10747+
Found by Jonathan Viquerat
in June 2026.