We develop high temperature series expansions for $ln{Z}$ and the uniform structure factor of the spin-half Heisenberg model on the hyperkagome lattice to order $beta^{16}$. These expansions are used to calculate the uniform susceptibility ($chi$), the entropy ($S$), and the heat capacity ($C$) of the model as a function of temperature. Series extrapolations of the expansions converge well down to a temperature of approximately $J/4$. A comparison with the experimental data for Na$_4$Ir$_3$O$_8$ shows that its magnetic susceptibility is reasonably well described by the model with an exchange constant $Japprox 300 K$, but there are also additional smaller terms present in the system. The specific heat of the model has two peaks. The lower temperature peak, which is just below our range of convergence contains about 40 percent of the total entropy. Despite being a 3-dimensional lattice, this model shares many features with the kagome lattice Heisenberg model and the material must be considered a strong candidate for a quantum spin-liquid.
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