The level of precision used for your survey depend on the estimated Crude Death Rate (number of deaths/10,000/day). If previous high quality mortality survey results are available it is best to use those results as a starting point and then estimate if the CDR has increased, decreased, or stayed the same.
Refer to 8.SM.02 ACF-CA Calculating Sample Size for Mortality for regional CDR estimates along with the following recommendations:
For most settings with death rates less than 1.0 deaths/10,000/day, a precision of ±0.3 is appropriate.
LOW: Where death rates are low (0.3 or less) greater precision maybe necessary: ± 0.2
HIGH: Where death rates are very high (> 1.0), a precision of ± 0.4 or 0.5 may be sufficient.
Do not use precision less than ± 0.2 unless there is strong justification.