Spins arranged on the kagome lattice are one of the most widely investigated topics in frustrated magnetism. In this context, the three-dimensional analogue of these systems, the hyperkagome lattice, offers an opportunity to study a similar topology with different constraints. Here we propose to study Na4Ir3O8: a spin-1=2 hyperkagome system that is thought to be a three-dimensional spin liquid.For Na4Ir3O8 the following questions remain significant and are suitable to be probed using muSR: - Can the absence of magnetic order down to low temperature be confirmed by a local probe? - Are the spin dynamics consistent with those of a three-dimensional spin liquid? - Is there any evidence for gapped spin excitations? - Do the spin excitations have a discontinuous temperature dependence indicative of a transitionbetween distinct fluctuating states?