1. A computer-implemented method, comprising: generating a grid of shards, the grid of shards forming a partitioned data set, the grid of shards being indexed by row and column, the grid of shards comprising a set of data shards, a set of derived shards, and a set of shards containing a predetermined data value, the set of derived shards comprising a set of horizontally-derived shards and a set of vertically-derived shards, wherein: the partitioned data set includes one or more shards containing one or more portions of the data set and one or more shards generated by applying an erasure code to the one or more shards containing the one or more portions of the data set; and each shard of the grid of shards has a corresponding row and corresponding column and is configured such that: the shard is reproducible from other shards associated with the row and reproducible from other shards associated with the column; if the shard is a horizontally-derived shard of the set of horizontally-derived shards, the shard is derived based at least in part on a set of data shards associated with the row; and if the shard is a vertically-derived shard of the set of vertically-derived shards, the shard is derived based at least in part on a set of shards associated with the column; and storing a data object using the grid of shards by at least: storing a copy of the data object in a storage device corresponding to a first shard of the grid of shards to produce an updated first shard, the updated first shard having a first corresponding row and a first corresponding column; updating a second shard of the grid of shards based at least in part on a first set of shards of the grid of shards, the first set of shards including the updated first shard and one or more shards of the set of shards containing the predetermined data value, each shard of the first set of shards having a same corresponding row as the second shard; updating a third shard of the grid of shards based at least in part on a second set of shards of the grid of shards, the second set of shards including the updated first shard and one or more shards of the set of shards containing the predetermined data value, each shard of the second set of shards having a same corresponding column as the third shard; and updating a fourth shard of the grid of shards based at least in part on a third set of shards of the grid of shards, the third set of shards including the updated second shard and one or more shards of the set of shards containing the predetermined data value, each shard of the third set of shards having the same corresponding column as the fourth shard.