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.
5. 
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 = 5.82002+
Found by Haowei Lin
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.
18. 
s = 6.25520+
Found by Vasily (Kotomord) Stolbov
in September 2026.
19. 
s = 6.39746+
Found by Joshua Wolk
in September 2026.
20. 
s = 6.51020+
Found by Joshua Wolk
in September 2026.
21. 
s = 6.63316+
Found by Joshua Wolk
in September 2026.
22. 
s = 6.71979+
Found by Joshua Wolk
in September 2026.
23. 
s = 6.86855+
Found by Joshua Wolk
in September 2026.
24. 
s = 7.00111+
Found by Joshua Wolk
in September 2026.
25. 
s = 7.13909+
Found by Joshua Wolk
in September 2026.
26.-27. 
s = 3 + 3√2 = 7.24264+
Found by Joshua Wolk
in September 2026.
28. 
s = 7.67360+
Found by Joshua Wolk
in September 2026.
29. 
s = 7.80858+
Found by Joshua Wolk
in September 2026.
30. 
s = 7.90931+
Found by Joshua Wolk
in September 2026.
31. 
s = 8.04264+
Found by Joshua Wolk
in September 2026.
32. 
s = 8.19030+
Found by Joshua Wolk
in September 2026.
33. 
s = 8.30128+
Found by Joshua Wolk
in September 2026.
34. 
s = 8.40134+
Found by Joshua Wolk
in September 2026.
35. 
s = 8.49650+
Found by Joshua Wolk
in September 2026.
36. 
s = 8.60297+
Found by Joshua Wolk
in September 2026.
37. 
s = 8.69283+
Found by Joshua Wolk
in September 2026.
38. 
s = 8.77541+
Found by Joshua Wolk
in September 2026.
39. 
s = 8.84087+
Found by Joshua Wolk
in September 2026.
40. 
s = 8.96390+
Found by Joshua Wolk
in September 2026.
41. 
s = 9.02962+
Found by Joshua Wolk
in September 2026.
42. 
s = 9.13440+
Found by Joshua Wolk
in September 2026.
43. 
s = 9.22307+
Found by Joshua Wolk
in September 2026.
44. 
s = 9.33610+
Found by Joshua Wolk
in September 2026.
45. 
s = 9.42855+
Found by Joshua Wolk
in September 2026.
46. 
s = 9.55330+
Found by Joshua Wolk
in September 2026.
47.-48. 
s = 4 + 4√2 = 9.65685+
Found by Joshua Wolk
in September 2026.
49. 
s = 9.93511+
Found by Joshua Wolk
in September 2026.
50. 
s = 10.04737+
Found by Joshua Wolk
in September 2026.