I have been playing around with Hastad's broadcast attack on RSA with linear padding. Using the implementation and the test function from here: https://github.com/0n5/CTF-Crypto/blob/master/RSA/hastads.sage
The test function and the attack work perfectly well with e=3,5,7. However, with e>=11 the attack does not find a solution. I tried playing around with the values of eps and modifying the attack to use more inputs (which shouldn't be needed), but the attack still fails.
Is there any reason for why the attack fails with a slightly larger e?