@article{23123,
  abstract     = {How many points can be placed in an 𝑛 × 𝑛 grid sothat every (affine) line contains at most 𝑘 points? Weprove that for 𝑛 ⩾ 𝑘 ⩾ 1037 the maximum number ofpoints is exactly 𝑘𝑛. Our proof builds on the recent workof Kovács, Nagy and Szabó (who proved an analogousresult when 𝑘 is at least about √𝑛 log 𝑛), incorporat-ing ideas of Jain and Pham. Using the same approach,we also obtain new bounds for higher-dimensionalextensions of this problem},
  author       = {Grebennikov, Aleksandr and Kwan, Matthew Alan},
  issn         = {1469-2120},
  journal      = {Bulletin of the London Mathematical Society},
  number       = {10},
  publisher    = {Wiley},
  title        = {{No‐(k+1)‐in‐line problem for large constant k}},
  doi          = {10.1112/blms.70510},
  volume       = {58},
  year         = {2026},
}