I did the math to show the aprox tx/s:
The block gas limit is 7,999,992
Transaction costs 21,000 gas (let's assume nothing else is attached)
That's ~380 transactions per block
With a block time of around 15.03 seconds. As https://ethstats.net/ shows.
This gives us aproximately: 25.346 tx/s.
At the end of your question, you have mentioned some possible ways to bring this number up.
- The more miners on the network, the more network difficulty, because difficulty calculation algorithms are always trying to make the next block's time be around 15s.
- More nodes will increase the block time even more because more delay between them will appear and then, more time will be needed for them to sync with each other.
There exists an inversely proportional relationship between the consensus volume and the tx/s rate. The more time the nodes need to accomplish the sync and achieve consensus, the less tx/s you will have.
To improve all of the features you mention, there are now a few ways on which Ethereum is entering:
- Sharding (Borns, while you realize that the whole blockchain can't process more transactions than a single node, can): "Solution" -> We split the state and history up into K = O(n / c) partitions that we call “shards”. For example, a sharding scheme on Ethereum might put all addresses starting with 0x00 into one shard, all addresses starting with 0x01 into another shard, etc. In the simplest form of sharding, each shard also has its own transaction history, and the effect of transactions in some shard k are limited to the state of shard k. One simple example would be a multi-asset blockchain, where there are K shards and each shard stores the balances and processes the transactions associated with one particular asset. In more advanced forms of sharding, some form of cross-shard communication capability, where transactions on one shard can trigger events on other shards, is also included.
Ethereum Fundation is donating lots of $ in order to incentivate the research on sharding and plasma.
Here I leave some really good github's info about sharding.
Another important improvement is the next:
- CasperFFG (As said before, PoW consensus algorithm is not scalable, because of that, new Proof of Concepts of consensus algorithms are being researched. Now Ethereum plans to move to PoS by implementing CasperFFG to start the transaction period on which 1/100 tx's will be done by PoS. Essentially it's a mixed PoW, PoS algorithm which it's purpose is to arrive one day to a PoS full implementation.) Solution -> By using PoS consensus algorithms, you eliminate the mining concept (as doing non-profitable calculations to find a hash in a certain range). Then, the block time can decrease till arriving at even 5 - 7s (Said by Vitalik Buterin).
Here I leave the CasperFFG paper's link.
There are more ideas to improve the speed of the network without losing it's main objective: consensus. But I posted the most important ones.
Hope it helps!