The current state of play :

- Code: Select all
` Status #Ranks`

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Grid exists 17812

No band exists 327

No grid exists 2 (*)

Unknown (LBC) 33

Unknown (HBC) 521

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18695

- (*) ranks 18601 and 18603 have been exhaustively searched (by BandKnit) and no grids found

- the missing ranks are divided into two categories, LBC for those ranks with low minlex band counts, and HBC for high minlex band counts.

Ranks greater than 18312 are LBC. These typically have 0 to 100 minlex bands. HBC ranks are 18312 and below, with band counts typically 100,000 and up.

The LBC missing ranks have all been tested for 1-ply grids, but full treatment with

BandKnit is out of the question, for reasons given above. Proving rank 18601 had no grids took nearly 100 core-days.

BandKnit is essentially a permutation cruncher, and it just might be possible to parallelise the computations, so a GPU might be able to make more rank proofs possible. That's just a germ of an idea at this stage ...