Popularity Block Labelling for Steiner Systems

Ordering 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 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).