Asymptotic Existence of Egalitarian Steiner 2-Designs

For an ordering of the blocks of a set system, each point has point sum equal to the sum of the indices of blocks containing that point. Improving access balancing for storage systems modelled as designs entails making these point sums as equal as possible. When all are equal, the system is egalitarian. It is established that the elementary necessary conditions for an egalitarian Steiner 2-design to exist are asymptotically sufficient.