  Optimising stellarators for quasisymmetry leads to strongly reduced
collisional transport and energetic particle losses compared to unoptimised
configurations. Though stellarators with precise quasisymmetry have been
obtained in the past, it remains unclear how broad the parameter space is where
good quasisymmetry may be achieved. We study the range of aspect ratio and
rotational transform values for which stellarators with excellent quasisymmetry
on the boundary can be obtained. A large number of Fourier harmonics is
included in the boundary representation, which is made computationally
tractable by the use of adjoint methods to enable fast gradient-based
optimisation, and by the direct optimisation of vacuum magnetic fields, which
converge more robustly compared to solutions from magnetohydrostatics. Several
novel configurations are presented, including stellarators with record levels
of quasisymmetry on a surface; three field period quasiaxisymmetric
stellarators with substantial magnetic shear, and compact quasisymmetric
stellarators at low aspect ratios similar to tokamaks.
