  We optimize the design of future spectroscopic redshift surveys for
constraining the dark energy via precision measurements of the baryon acoustic
oscillations (BAO), with particular emphasis on the design of the Wide-Field
Multi-Object Spectrograph (WFMOS). We develop a model that predicts the number
density of possible target galaxies as a function of exposure time and
redshift. We use this number counts model together with fitting formulae for
the accuracy of the BAO measurements to determine the effectiveness of
different surveys and instrument designs. We search through the available
survey parameter space to find the optimal survey with respect to the dark
energy equation-of-state parameters according to the Dark Energy Task Force
Figure-of-Merit, including predictions of future measurements from the Planck
satellite. We optimize the survey to test the LambdaCDM model, assuming that
galaxies are pre-selected using photometric redshifts to have a constant number
density with redshift, and using a non-linear cut-off for the matter power
spectrum that evolves with redshift. We find that line-emission galaxies are
strongly preferred as targets over continuum emission galaxies. The optimal
survey covers a redshift range 0.8 < z < 1.4, over the widest possible area
(6000 sq. degs from 1500 hours observing time). The most efficient number of
fibres for the spectrograph is 2,000, and the survey performance continues to
improve with the addition of extra fibres until a plateau is reached at 10,000
fibres. The optimal point in the survey parameter space is not highly peaked
and is not significantly affected by including constraints from upcoming
supernovae surveys and other BAO experiments.
