We investigate the behavior of f(d), the least size of a lattice of order dimension d. In particular we show that the lattice of a projective plane of order n has dimension at least n/ln(n), so that f(d)=O(d)2 log2d. We conjecture f(d)=θ(d2), and prove something close to this for height-3 lattices, but in general we do not even know whether f(d)/d→∞.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology
- Computational Theory and Mathematics
- AMS subject classifications (1980): 06A10, 06A23
- least size
- order dimension