  We have used semi-synthetic records of emerging sunspot groups based on
sunspot number data as input for a surface flux transport model to reconstruct
the evolution of the large-scale solar magnetic field and the open heliospheric
flux from the year 1700 onward. The statistical properties of the
semi-synthetic sunspot group records reflect those of the observed the Royal
Greenwich Observatory photoheliographic results. These include correlations
between the sunspot numbers and sunspot group latitudes, longitudes, areas and
tilt angles. The reconstruction results for the total surface flux, the polar
field, and the heliospheric open flux (determined by a current sheet source
surface extrapolation) agree well with the available observational or
empirically derived data and reconstructions. We confirm a significant positive
correlation between the polar field during activity minimum periods and the
strength of the subsequent sunspot cycle, which has implications for flux
transport dynamo models for the solar cycle. Just prior to the Dalton minimum,
at the end of the 18th century, a long cycle was followed by a weak cycle. We
find that introducing a possibly `lost' cycle between 1793 and 1800 leads to a
shift of the minimum of the open flux by 15 years which is inconsistent with
the cosmogenic isotope record.
