  We study the zero-temperature phase diagram and the low-lying excitations of
a square-lattice spin-half Heisenberg antiferromagnet with two types of
regularly distributed nearest-neighbour exchange bonds (J>0 (antiferromagnetic)
and J'>0, J'<0) using the coupled cluster method (CCM) for high orders of
approximation (up to LSUB8). We use a Neel model state as well as a helical
model state as a starting point for the CCM calculations. We find a
second-order transition from a phase with Neel order to a finite-gap quantum
disordered phase for sufficiently large antiferromagnetic exchange constants
J'>0. For frustrating ferromagnetic couplings J'<0 we find indications that
quantum fluctuations favour a first-order phase transition from the Neel order
to a quantum helical state, by contrast with the corresponding second-order
transition in the corresponding classical model. The results are compared to
those of exact diagonalizations of finite systems (up to 32 sites) and those of
spin-wave and variational calculations. The CCM results agree well with the
exact diagonalization data over the whole range of the parameters. The special
case of J'=0, which is equivalent to the honeycomb lattice, is treated more
closely.
