Laser-induced fluorescence to the electronic ground state (X)11Σ+ of LiNa has been recorded by a Fourier-transform spectrometer. Optical excitations of the LiNa molecules into the (A)21Σ+ state were performed with different dye lasers. The spectra showed fluorescence progressions up to v''=44 of the singlet ground state covering 99.9% of the potential well. However, searches for fluorescence into the triplet ground state (a)13Σ+ induced by spin-orbit coupling in the excited system (b)13Π-(A)21Σ+ were not successful. The potential energy curve of the singlet ground state was determined by direct potential fits with a data set of about 8200 assigned lines using two distinct analytical potential representations. In addition, the isotopologue 6Li23Na was studied for a possible need of Born-Oppenheimer corrections by simultaneous fits of both observed isotopologues from 6Li and 7Li. Finally, new data on Feshbach resonances from cold-atom experiments at Heidelberg were included for improving the potential description around the dissociation energy for both electronic states (X)11Σ+ and (a)13Σ+ of the atom-pair ground-state asymptote.