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Currently, the gas limit imposes an upper bound on the amount of computation that can be done in an Ethereum smart contract. Part of the purpose of this limit is to upper-bound the burden on miners and verifiers.

There are various proposals for sharding, which would allow the Ethereum blockchain to scale to a larger number of transactions. Would sharding allow increasing the gas limit? Do any of the existing sharding proposals propose to increase the gas limit, and by how much?

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Yes, the gas limit could be increased roughly by a factor that is proportional to the number of shards, which is planned to be 100. FMI, see https://github.com/ethereum/wiki/wiki/Sharding-introduction-R&D-compendium.

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