Let be a finite field, and let (ℙ, ] be a nontrivial 2-(n, k, 1)-design over . Then each point α ∈ ℙ induces a (k - 1)-spread Sα on ℙ/α. (ℙ, ) is said to be a geometric design if Sα is a geometric spread on ℙ/α for each α isin; ℙ. In this paper, we prove that there are no geometric designs over any finite field .
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Designs over finite fields
- Partial geometries