Disk covering problem $r(10)$

The smallest value $r(10)$ such that $10$ disks of radius $r(10)$ can be arranged to cover the unit disk.

Value: ${\approx}0.394930$

Updates

Upper bound: ${\approx}0.394930$
Reference unknown
[via Circles Covering Circles, Erich Friedman]
2005 Lower bound: ${\approx}0.394930$
Gábor Fejes Tóth in 2005
[via Circles Covering Circles, Erich Friedman]