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P=216 Candidate Catalog

This page records the P=216 candidates encountered during the structural and decoder-failure screening runs. Screened-out rows are retained here for provenance, but they are not promoted to the main live table. The main P=216 row remains the UB6-screened seed 17265506054090875 with decoder-fail UB 14.

April 13, 2026 update: a cheap structural recomputation of the six recently collected 3Mac rows leaves only seed 17265494505985185 structurally above the current P=216 best bound; however, existing \(p=0.03\) 3Mac decoder-fail logs contain valid syndrome-matched logical witnesses of weight 10 for that seed. The other five collected rows drop to \(12\) or \(8\) by \(m\)-block/direct structural checks. Existing UB6 logs already screen the remaining catalogued rows to weights at most 14, so no paid TSUBAME UB6 job was launched from this filter step.

Candidate Table

This page uses the same table structure as the main live table. Red-tinted rows are screened-out candidates; their small upper bounds are useful negative evidence, not current best records.

P Current best code Seed Latent UB m-block UB CRT UB Cycle-8 ETS UB Direct CSS UB Decoder-fail UB Completed at p=0.03 Completed at p=0.04
216 (current best) \(\left[\left[2592,1300,\leq 14\right]\right]\) 17265506054090875 24 36 54 NE 54 14 >10.55M --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265494505985185 36 18 64 NE 54 10 valid 3Mac logical hits --
216 (screened) \(\left[\left[2592,1300,\leq 12\right]\right]\) 17265494505985345 24 12 32 NE 12 -- -- --
216 (screened) \(\left[\left[2592,1300,\leq 8\right]\right]\) 17265506054091336 24 8 16 NE 24 -- -- --
216 (screened) \(\left[\left[2592,1300,\leq 8\right]\right]\) 17265506054091584 24 8 16 NE 18 -- -- --
216 (screened) \(\left[\left[2592,1300,\leq 8\right]\right]\) 17265506054091610 24 8 -- NE -- -- -- --
216 (screened) \(\left[\left[2592,1300,\leq 8\right]\right]\) 17265506054091687 24 8 16 NE 18 -- -- --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265506054377620 36 18 -- NE -- 6 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265506054449587 24 18 -- NE -- 10 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265506054737541 36 18 -- NE -- 6 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265506055137358 36 18 -- NE -- 10 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265506055177557 36 18 -- NE -- 8 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 16\right]\right]\) 17265506055217710 36 16 -- NE -- 6 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265506055393325 36 18 -- NE -- 10 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265506055505346 36 18 -- NE -- 10 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 24\right]\right]\) 17265506055545674 24 36 -- NE -- 12 hit found --
216 (screened) \(\left[\left[2592,1300,\leq 18\right]\right]\) 17265506055945409 24 18 -- NE -- 14 hit found --