New limits on spatial anisotropy from optically-pumped<i>sup201</i>Hg and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Hg</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>199</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

The nuclear magnetic resonance frequencies of $^{201}\mathrm{Hg}$ (I=(3/2)) and $^{199}\mathrm{Hg}$ (I=(1/2)) have been compared by use of optically pumped atomic light absorption oscillators to see if the relative frequencies depend on the orientation of the quantization axis in space. The null result \ensuremath{\delta}${\ensuremath{\nu}}_{2}$5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ Hz improves by over 3 orders of magnitude recent limits on any quadrupolar interactions violating spatial isotropy, and can be interpreted as the most precise test yet of local Lorentz invariance. The experiment also improves the limits on anisotropic dipole interactions.