1. A computer-implemented method, comprising: generating a first grid of shards, the first grid of shards indexed by row and column, the first grid of shards comprising a first set of data shards and a first set of derived shards, the first set of derived shards comprising a first set of horizontally-derived shards and a first set of vertically-derived shards, wherein each shard of the first grid of shards has a corresponding datacenter location, a corresponding row, and corresponding column and is configured such that: the shard is reproducible from other shards associated with the row corresponding to the shard of the first grid of shards using a first redundancy code and reproducible from other shards associated with the column corresponding to the shard of the first grid of shards using a second redundancy code; generating a second grid of shards, the second grid of shards indexed by row and column, the second grid of shards comprising a second set of data shards and a second set of derived shards, the second set of data shards including at least twice as many data shards as the first set of data shards, the second set of data shards including the first set of data shards, the second set of derived shards comprising a second set of horizontally-derived shards and a second set of vertically-derived shards, wherein each shard of the second grid of shards has a corresponding datacenter location, a corresponding row, and corresponding column and is configured such that: the shard is reproducible from other shards associated with the row corresponding to the shard of the second grid of shards using a third redundancy code and reproducible from other shards associated with the column corresponding to the shard of the second grid of shards using the second redundancy code; deriving a horizontally-derived shard in the second grid of shards by at least: selecting a first set of shards of the second grid of shards based at least in part on having the same corresponding row as the horizontally-derived shard; and reproducing the horizontally-derived shard from a subset of the first set of shards based at least in part on the third redundancy code; deriving a vertically-derived shard in the second grid of shards by at least: selecting a second set of shards of the second grid of shards based at least in part on having the same corresponding column as the vertically-derived shard; and reproducing the vertically-derived shard from a subset of the second set of shards based at least in part on the first redundancy code; and storing, on one or more storage devices corresponding to datacenter locations of the second grid of shards, the second grid of shards.