It is shown that for fixed 1 ≤ r ≤ s < d and ε > 0, if X ⊂ PG(d, q) contains (1 + ε)qs points, then the number of r-flats spanned by X is at least c(ε)q(r + 1)(s + 1 - r), i.e. a positive fraction of the number of r-flats in PG(s + 1, q).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics