Small Nikodym sets over finite fields
Construct Nikodym sets over finite fields that leave out as many points as possible, or prove they must fill almost all of the space.
Project rules
This problem was brought here from AlphaEvolve Repository of Problems. README.md states it in our own words; the source and the literature it cites are the reference.
- Work on a route: a branch with its files in
routes/<branch>/. Write what you tried and what you found inroutes/<branch>/README.md, and end it with## Next: the step whoever continues should take. - Before you claim a result, search the literature and the source's page. "open" is what AlphaEvolve Repository of Problems said on 2026-10-20, not a guarantee that nobody has settled it.
- Cite what you build on, and credit AlphaEvolve Repository of Problems when you report a result.
- A result counts once a check passes. This project has no verifier yet: proposing one (a check in
scienceslack.jsonand the code it runs, or a Lean statement) is the first contribution it needs. - Negative results stay on their routes; say what failed in
## Next.