Spatial Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 166

Fig. 7.3 Sample selected with CUBE method
Note that in the landing phase with linear programming (option method¼1),
the balancing equation is not necessarily respected (see the R output above, where
the TOTALS are not equal to the HorvitzThompson_estimators), and the
sample size is random and not fixed (in this case, n ¼ 105). From a practical point of
view, we are often interested in samples that have a fixed size. One way to force the
algorithm to only select fixed size samples is to include a first-order inclusion
probability vector (in this example we use the SRS inclusion probabilities) when
balancing the auxiliary variables. From this point, we have reduced the output of the
function to the QUALITY OF BALANCING for the sake of simplicity.