The following pictures show n unit octagons packed inside the smallest known hexagons (with side s).
1. 
s = cos(7.5°)/√3/sin(22.5°) = 1.49578+
Trivial.
2. 
s = 2.70289+
Trivial.
3. 
s = 2.88958+
Found by Mohamed Metwalli
in June 2026.
4. 
s = 11+8√2–16/√3–4√6 = 3.27814+
Found by Mohamed Metwalli
in June 2026.
5. 
s = 3.71848+
Found by Jonathan Viquerat
in June 2026.
6. 
s = 3.94730+
Found by Aristotle Papowitz
in July 2026.
7. 
s = 3.97716+
Found by Jonathan Viquerat
in June 2026.
8. 
s = 4.56653+
Found by Jonathan Viquerat
in June 2026.
9. 
s = 4.93304+
Found by Jonathan Viquerat
in June 2026.
10. 
s = 5.06929+
Found by Jonathan Viquerat
in June 2026.
11. 
s = 5.34796+
Found by Bhavithran Ananthan
in July 2026.
12. 
s = 5.38669+
Found by Jonathan Viquerat
in June 2026.
13. 
s = 5.75470+
Found by Jonathan Viquerat
in June 2026.
14. 
s = 5.77752+
Found by Jonathan Viquerat
in June 2026.
15. 
s = 6.13744+
Found by Bhavithran Ananthan
in June 2026.
16. 
s = 6.21438+
Found by Jonathan Viquerat
in June 2026.
17. 
s = 6.35723+
Found by Joshua Wolk in September 2026.
18. 
s = 6.42774+
Found by Bhavithran Ananthan
in July 2026.
19. 
s = 6.44696+
Found by Bhavithran Ananthan
in July 2026.
20. 
s = 6.99419+
Found by Leo Strijbos
in August 2026.
21. 
s = 7.06795+
Found by Joshua Wolk in September 2026.
22. 
s = 7.32810+
Found by Joshua Wolk in September 2026.
23. 
s = 7.43164+
Found by Joshua Wolk in September 2026.
24. 
s = 7.53131+
Found by Joshua Wolk in September 2026.
25. 
s = 7.74422+
Found by Joshua Wolk in September 2026.
26. 
s = 7.84079+
Found by Joshua Wolk in September 2026.
27. 
s = 7.86114+
Found by Joshua Wolk in September 2026.
28. 
s = 8.14118+
Found by Joshua Wolk in September 2026.
29. 
s = 8.24943+
Found by Joshua Wolk in September 2026.
30. 
s = 8.27001+
Found by Joshua Wolk in September 2026.
31. 
s = 8.55448+
Found by Joshua Wolk in September 2026.
32. 
s = 8.63669+
Found by Joshua Wolk in September 2026.
33. 
s = 8.69106+
Found by Joshua Wolk in September 2026.
34. 
s = 8.79338+
Found by Joshua Wolk in September 2026.
35. 
s = 8.86335+
Found by Joshua Wolk in September 2026.
36. 
s = 8.92001+
Found by Joshua Wolk in September 2026.
37. 
s = 8.93472+
Found by Joshua Wolk in September 2026.
38. 
s = 9.36761+
Found by Joshua Wolk in September 2026.
39. 
s = 9.50169+
Found by Joshua Wolk in September 2026.
40. 
s = 9.55404+
Found by Joshua Wolk in September 2026.
41. 
s = 9.77460+
Found by Joshua Wolk in September 2026.
42. 
s = 9.85080+
Found by Joshua Wolk in September 2026.
43. 
s = 9.92753+
Found by Joshua Wolk in September 2026.
44. 
s = 9.99809+
Found by Joshua Wolk in September 2026.
45. 
s = 10.18798+
Found by Joshua Wolk in September 2026.
46. 
s = 10.26603+
Found by Joshua Wolk in September 2026.
47. 
s = 10.32874+
Found by Joshua Wolk in September 2026.
48. 
s = 10.35305+
Found by Joshua Wolk in September 2026.
49. 
s = 10.58403+
Found by Joshua Wolk in September 2026.
50. 
s = 10.66657+
Found by Joshua Wolk in September 2026.