How Does Sharding Increase Bandwidth From 15 TPS to 100,000 TPS?

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I know how sharding works at a high level, but I'd like a more technical explanation - especially on how we can get to 100,000 transactions per second. From my understanding, EIP-4844 proposes an increase to the size of blocks by an additional 2MB. Since blocks are already \~2MB, this will double the block size to \~4MB. The additional 2MB allows space for 16 'blobs' which follow an alternate gas price model. But how does this increase TPS by such a large magnitude? If I assume each blob can do 15 TPS, this increases TPS to 15\*16 = 240. Can someone help me with the maths?