Unresolved orders in the cubic (3,11)-spectrum

Determine whether cubic graphs of girth 11 exist at every even order from 128 through 142.

Background

The (3,11)-cage has order 112, and the paper gives an upper bound N(3,11)≤144. However, the even orders immediately above the known range, namely 128 through 142, have neither been realized by constructions nor excluded by nonexistence arguments.

References

The $(3,11)$-graphs of even orders $128$ through $142$ are yet to be found or excluded.

— Theoretical and Computational Approaches to Determining Sets of Orders for $(k,g)$-Graphs  (2503.06466 - Eze et al., 9 Mar 2025) in Section 3.1, subsection “(3,11)-Spectrum”