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The existence of subspace designs

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arxiv 2212.00870 v2 pith:MPCJCVNK submitted 2022-12-01 math.CO

Peter Keevash , Ashwin Sah , Mehtaab Sawhney This is my paper · ORCID
classification math.CO
keywords designsexistenceparameterssubspaceapproximateconditionsdesigndimension
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We prove the existence of subspace designs with any given parameters, provided that the dimension of the underlying space is sufficiently large in terms of the other parameters of the design and satisfies the obvious necessary divisibility conditions. This settles an open problem from the 1970s. Moreover, we also obtain an approximate formula for the number of such designs.

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  1. A short proof of the existence of designs

    math.CO 2024-11 accept novelty 6.0 of 10

    Keevash proves the existence of designs with a shorter self-contained proof, using a new absorber construction and improving the bound on n0.

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