Generation of magnetic field energy, without mean field generation, is
studied. Isotropic mirror-symmetric turbulence of a conducting fluid
amplifies the energy of small-scale magnetic perturbations if the magn
etic Reynolds number is high, and the dimensionality of space d satisf
ies 2.103 < d < 8.765. The result does not depend on the model of turb
ulence, incompressibility, and isotropy being the only requirements.