Using a modified windowed reouting approach (described here) with the marginal-forbidden heuristic (described here), I was able to find some more improvements to snake-in-the-box, coil-in-the-box, and symmetric coil-in-the-box records.
Improvements to the 13-d snake-in-the-box construction were marginal, improving my existing length-2898 snake into a length-2900 snake.
| n | previous-best length | new snake length |
|---|---|---|
| 13 | 2898 | 2900 |
Ace's 13-d length-2832 coil, first published at www.minortriad.com/snake/, was improved to a length-2840 coil.
| n | previous-best length | new coil length |
|---|---|---|
| 13 | 2832 | 2840 |
This search method was most effective for symmetric coils, improving two of my existing constructions. I suspect this is primarily due to two factors: (1) symmetric coils have been given relatively little attention, and as a result they are not deeply-embedded local optima; (2) an implicit-quotient approach halves the effective beam search depth.
| n | previous-best length | new coil length | % of general coil† |
|---|---|---|---|
| 12 | 1422 | 1430 | 99.2% (1430/1442) |
| 13 | 2766 | 2810 | 98.9% (2810/2840) |
†As of the time of writing, July 8, 2026, per www.minortriad.com/snake/.
Last updated July 8, 2026