Egalitarian Steiner triple systems for data popularity

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)/2log 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.