For an ordering of the blocks of a design, the point sum of an element is the sum of the indices of blocks containing that element. Block labelling for popularity asks for the point sums to be as equal as possible. For Steiner systems of order v and strength t in general, the average point sum is \(O(v^{2t-1})\); under various restrictions on block partitions of the Steiner system, the difference between the largest and smallest point sums is shown to be \(O(v^{(t+1)/2}\log v)\). Indeed for Steiner triple systems, direct and recursive constructions are given to establish that systems exist with all point sums equal for more than two thirds of the admissible orders.

对于设计块的排序，元素的点总和是包含该元素的块的索引总和。受欢迎程度的块标记要求点总和尽可能相等。对于一般为v阶且强度为t 的Steiner 系统，平均点和为\(O(v^{2t-1})\)；在 Steiner 系统的块分区的各种限制下，最大和最小点和之间的差异显示为\(O(v^{(t+1)/2}\log v)\)。实际上，对于 Steiner 三重系统，给出了直接和递归构造以建立所有点和等于超过三分之二的可接受阶数的系统存在。