The reaction, part of the neon-sodium cycle of hydrogen burning, may explain the observed anticorrelation between sodium and oxygen abundances in globular cluster stars. Its rate is controlled by a number of low-energy resonances and a slowly varying nonresonant component. Three new resonances at , 189.5, and 259.7 keV have recently been observed and confirmed. However, significant uncertainty on the reaction rate remains due to the nonresonant process and to two suggested resonances at and 105 keV. Here, new data with high statistics and low background are reported. Stringent upper limits of and (90% confidence level), respectively, are placed on the two suggested resonances. In addition, the off-resonant factor has been measured at unprecedented low energy, constraining the contributions from a subthreshold resonance and the direct capture process. As a result, at a temperature of 0.1 GK the error bar of the rate is now reduced by 3 orders of magnitude.