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This paper details the solar neutrino analysis of the 385.17-day Phase-IIIdata set acquired by the Sudbury Neutrino Observatory (SNO). An array of $^3$Heproportional counters was installed in the heavy-water target to measureprecisely the rate of neutrino-deuteron neutral-current interactions. Thistechnique to determine the total active $^8$B solar neutrino flux was largelyindependent of the methods employed in previous phases. The total flux ofactive neutrinos was measured to be$5.54^{+0.33}_{-0.31}(stat.)^{+0.36}_{-0.34}(syst.)\times 10^{6}$ cm$^{-2}$s$^{-1}$, consistent with previous measurements and standard solar models. Aglobal analysis of solar and reactor neutrino mixing parameters yielded thebest-fit values of $\Delta m^2 = 7.59^{+0.19}_{-0.21}\times 10^{-5}{eV}^2$ and$\theta = 34.4^{+1.3}_{-1.2}$ degrees.

Measurement of the $\nu_e$ and Total $^{8}$B Solar Neutrino Fluxes with the Sudbury Neutrino Observatory Phase-III Data Set