I analysed bases with different systems for denominations of currency or weights. I chose to investigate denominations incrementing approximately logarithmically and are rounded to a near factor of the base.
If the base is a power of two, and the denominations are all the factors of the base, the system is efficient because there would be neither more nor fewer than are needed to make up any amount.
Bases with systems of denominations that are deficient require some of the denominations to be available more than once in order to be able to make up any amount.
Sufficient systems do not require more than one copy of any of their denominations. However, they may lack efficiency by having more denominations or kinds of value than are necessary to make up amounts.
It is better for a system to be sufficient than deficient.
By this analysis, decimal is deficient and requires carrying more weight items than an efficient system.
There is a dozenal system that is sufficient and is nearly efficient because its denominations sum to the base. The results show that dozenal requires fewer coins or weights to be carried than decimal to make up any amount up to a given value, because the number of amounts that can be made using the same number of weights is superior for the dozenal system.
I omitted to show in the table that the base of the exponential sequence for the decimal pseudosexagesimal can be approximated by the fourth root of ten.
There is also a system based on the gross. Its exponential base is about the seventh root of the square of a dozen. This system is slightly deficient and up to its base requires one denomination to be duplicated, giving a total of nine weights, which is the same as for the equivalent amount in the dozenal system. However, the sum of the weights in the dozenal can reach a slightly higher value and hence can represent more amounts than the gross system. Nevertheless, the gross system is more efficient than decimal.
The value for the third power in the sixth root sexagesimal system could be either ten or six, affecting which denomination is required in double stock; just a little something extra to think about.