W-0078
A superpermutation on 8 symbols, found by Theo H.. It beat the previous record, W-0077, by 1 letter, and is the record for n = 8.
- Length
- 46,173
- Repeated occurrences
- 56
- Announced
- Oct 20, 2026
012345670123456071234560172345601273456012374560123475601234576012345067123450617234506127345061237450612347506123457061…
Windows
| 46,166 | windows of 8 consecutive letters | |
| = | 40,320 | distinct permutations, all 8! of them |
| + | 56 | repeated occurrences of a permutation |
| + | 5,790 | windows that are not permutations |
How it was found
Halfar's 16 closed trails, unchanged, in a new order and with new openings, found with Halfar's unchanged trailsearch.c on his selection: three trails open at a weight-2 step, so the openings cost 3 letters more and the joins 4 less. 56 repeated permutations.
Checking
Total check time: under 1 s, including preparation but not time in the queue.
| Program | Source | Result | Time |
|---|---|---|---|
| classcheck | 41928cce | all 40,320 permutations appear, by rotation class | under 1 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | under 1 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | under 1 s |
Download
Download Detour (.detour) 284 bytes, or 46.2 kB decoded
Download text (.txt) 46.2 kB
# check it yourself
detour decode W-0078.detour - | tr -d '\n' | shasum -a 256
tar xzf checkers-rs-source.tar.gz && cd checkers-rs && cargo build --release --locked
./target/release/classcheck 8 ../W-0078.detour 46173
./target/release/bitmapcheck 8 ../W-0078.detour 46173
./target/release/wordhash 8 ../W-0078.detour 46173
Decoding needs detour; see the Detour format for how to build and install it. The checkers are in checkers-rs-source.tar.gz, which needs Rust 1.89 or later; each one decodes the file itself, so the word is never written out.
The file's header gives n = 8 and sync exponent 0. The file has 917 tokens: 1 START, 1 literal of 1 byte in all, and 915 deviations. Deviations by weight, from 1 to 8: 56 · 208 · 645 · 1 · 3 · 2 · 0 · 0.