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That left a sparse hodgepodge of subspaces that they still had to deal with.
Source: https://www.wired.com/story/mathematicians-find-hidden-structure-in-a-common-type-of-space/
They then applied a modified version of a fundamentally random process called the Rödl nibble to cover most of the remaining subspaces.
Source: https://www.wired.com/story/mathematicians-find-hidden-structure-in-a-common-type-of-space/