  We report magnetic susceptibility (chi) and heat capacity Cp measurements
along with ab-initio electronic structure calculations on PbCuTe2O6, a compound
made up of a three dimensional 3D network of corner-shared triangular units.
The presence of antiferromagnetic interactions is inferred from a Curie-Weiss
temperature (theta_CW) of about -22 K from the chi(T) data. The magnetic heat
capacity (Cm) data show a broad maximum at T^max ~ 1.15 K (i.e. T^max/theta_CW
~ 0.05), which is analogous to the the observed broad maximum in the Cm/T data
of a hyper-Kagome system, Na4Ir3O8. In addition, Cm data exhibit a weak kink at
T^* ~ 0.87 K. While the T^max is nearly unchanged, the T^* is systematically
suppressed in an increasing magnetic field (H) up to 80 kOe. For H > 80 kOe,
the Cm data at low temperatures exhibit a characteristic power-law (T^{\alpha})
behavior with an exponent {\alpha} slightly less than 2. Hopping integrals
obtained from the electronic structure calculations show the presence of
strongly frustrated 3D spin interactions along with non-negligible unfrustrated
couplings. Our results suggest that PbCuTe2O6 is a candidate material for
realizing a 3D quantum spin liquid state at high magnetic fields.
