  We study a new type of extremal problem in complex analysis, referred to as
"geometric zero packing", which is the hyperbolic analogue of a problem
considered by Abrikosov in the 1950s concerning Bose-Einstein condensates. We
relate the corresponding minimal discrepancy density with the asymptotic
variance for Bloch functions of the form "Bergman projection of bounded
functions" and obtain a corresponding identity. Together with related work of
Ivrii, this gives the asymptotic behavior of the universal quasiconformal
integral means spectrum for small values of quasiconformality k and small
exponents t. In particular, the conjectured behavior is shown to be smaller
than conjectured by Prause and Smirnov, which also shows that there are no
quasidisks with dimension 1+k^2, at least for small k.
