Cage order $n(4,12)$

The order of a $(4,12)$-cage, a $4$-regular graph of girth $12$ of minimum order.

Updates

• Lower bound: $728$
  Reference unknown
  [via Cage (graph theory) - Wikipedia]
• Upper bound: $728$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]