The existence of subspace designs

Keevash, Peter; Sah, Ashwin; Sawhney, Mehtaab

doi:https://doi.org/10.1112/plms.70071

The existence of subspace designs

Download

Name

Proceedings of London Math Soc - 2025 - Keevash - The existence of subspace designs.pdf

Size

772.82 KB

Format

Adobe PDF

Checksum (MD5)

fb3ae8f23ed2fd82b072306f58a49c02

Author(s)

Keevash, Peter

•

Sah, Ashwin

•

Sawhney, Mehtaab

Date Issued

July 17, 2025

Journal

Proceedings of the London Mathematical Society

Publisher

Wiley

Citation

Keevash, P., Sah, A. and Sawhney, M. (2025), The existence of subspace designs. Proc. London Math. Soc., 131: e70071.

Version

Final published version

Abstract

We prove the existence of subspace designs with anygiven parameters, provided that the dimension of theunderlying space is sufficiently large in terms of theother parameters of the design and satisfies the obvi-ous necessary divisibility conditions. This settles an openproblem from the 1970s. Moreover, we also obtain anapproximate formula for the number of such designs.

MIT Department

Massachusetts Institute of Technology. Department of Mathematics

Terms of Use

Creative Commons Attribution

https://creativecommons.org/licenses/by/4.0/

Persistent DSpace Link

https://hdl.handle.net/1721.1/163394

DOI of Published Version

https://doi.org/10.1112/plms.70071