Creating a function for Automatic optimal stratification

Question

Sample data:

dat <- as.data.frame(runif(100000, 0, 3000))
names(dat)[1] <- "Y"
dat$type <- sample(LETTERS, 100000, replace = TRUE)
dat$region <- stri_rand_strings(100000, 1, "[A-D]")

setDT(dat)
dat[, `:=` (count_by_type = .N, var_Y = var(Y)), by = type]

I would like to write a function that does the process of optimal stratification for me. It should essentially check whether the variance decreases by more than 5%, when and extra stratum is added.

The requirements are as follows:

The maximum amount of groups is 8, which would then have the following cut-off points

max_stratums <- c(50, 100, 250, 500, 750, 1000, 1500, 3000)

There is a minimum amount of observations per group is 200. I thought of doing something like creating a function below;

optimal_strat <- function(dat, max_stratums) {
    for i in max_stratums {

        # Loop through possible cut-off points
        setDT(dat)[, SO_cat := cut2(Y, max_stratums[i])]

        # Calculate variance for new division
        dat[, `:=` (sub_type = .N, var_Y2 = var(Y)), by = c("SO_cat", "type")]

        # Now I need to compare if the weighted variance of one of the divisions is 5% less than the old and pick the division with the biggest weighted decrease. Something like:
        dat[var_Y_2 > var_Y2, 

    }
}

How should I code this last part?

Ideally the function would not run once, but until the variance per group no longer decreases enough..