New calibrations for estimating the N/O ratio in HII regions

We use a sample of 536 \hii\ regions located in nearby spirals, with an homogeneous determination of their $T_e$-based abundances, to obtain new empirical calibrations of the N2O2, N2S2, O3N2, and N2 strong-line indices to estimate the nitrogen-to-oxygen abundance ratio when auroral lines are not detected. All indices are strongly correlated with the $T_e$-based $\log$(N/O) for our \hii\ region sample, even more strongly than with $12+\log$(O/H). N2O2 is the most strongly correlated index, and the best fit to the $\log$(N/O)-N2O2 relation is obtained with a second-order polynomial. The derived relation has a low dispersion ({\em rms}$<$0.09~dex), being valid in the range $-1.74 <$ N2O2 $< 0.62$ (or $-1.81 <$ $\log$(N/O) $< -0.13$). We have compared our calibration with previous ones and have discussed the differences between them in terms of the nature of the objects used as calibrators.