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Diamonds can be found in levels below 16, but when it comes to limited mining, a 3-by-1 tunnel can be done on levels 10,11, and 12 for a maximum number of diamonds. Level 12 has the highest chance of spawning.
MineCraft username: RedFollower68. I think you probably would have better luck closer to the surface because you'll be finding the same amount of blocks, but it will just be iron and coal compared to lower levels where the blocks are split up between iron, coal, redstone, diamond, lapis lazuli, and gold.