The following pictures show n unit octagons packed inside the smallest known domino (with short side s).
1-2. 
s = 1 + √2 = 2.41421+
Trivial.
3. 
s = 3.51367+
Found by Jonathan Viquerat
in May 2026.
4. 
s = 3.97990+
Found by Jonathan Viquerat
in May 2026.
5. 
s = 4.28798+
Found by Jonathan Viquerat
in May 2026.
6. 
s = 4.50805+
Found by Jonathan Viquerat
in May 2026.
7.-8. 
s = 2 + 2√2 = 4.82842+
Trivial.
9. 
s = 5.49509+
Found by Jonathan Viquerat
in May 2026.
10. 
s = 3 + 2√2 = 5.82842+
Found by Jonathan Viquerat
in May 2026.
11. 
s = 6.02842+
Found by Jonathan Viquerat
in May 2026.
12. 
s = 6.31126+
Found by Jonathan Viquerat
in May 2026.
13.-14. 
s = 6.51126+
Found by Jonathan Viquerat
in May 2026.
15. 
s = 6.77016+
Found by Jonathan Viquerat
in May 2026.
16. 
s = 7.10456+
Found by Jonathan Viquerat
in May 2026.
17.-18. 
s = 3 + 3√2 = 7.24263+
Trivial.
19. 
s = 7.77123+
Found by Jonathan Viquerat
in May 2026.
20. 
s = 8.03947+
Found by Jonathan Viquerat
in May 2026.