Minimal superpermutation length $L(2)$

The shortest length of a string that contains each permutation of $2$ symbols as a substring.

Updates

• Lower bound: $3$
  Trivial or easy according to the secondary source.
  [via Superpermutations - Greg Egan]
• Upper bound: $3$
  Trivial or easy according to the secondary source.
  [via Superpermutations - Greg Egan]