It is often recommend to use the estimate of variance based on simple random sampling without replacement when a systematic sample is drawn. The following code computes the true variance under both designs of sample mean as an estimate of the population mean. The function varsystematic returns the true variance for the systematic design first followed by the true variance under simple random sampling without replacement.
If N is the population size and n is the sample size then k=N/n is the number of possible systematic samples.