Noise growth upon realignment of FV

I’m going through the [FV scheme]( and SEAL and there are a few things I don’t understand regarding noise growth or realignment. * On page 8 they say to choose * T * so that the noise growth from realignment is similar to that from multiplication. Why do we want noise growth to be as small as possible and not as small as possible? On page 9, they go on to say that if they pick a big T, they get a big realignment noise, but then all subsequent realignments don’t cause the noise to increase? How is this? I multiply c1 * c2, realign, then multiply that by c3 and realign again, why wouldn’t the noise increase? * On page 11, first paragraph after entry 3, they state that they can ignore the realignment noise because it is less than multiplication. Why can they ignore it? Isn’t that making the binding on || v_mul || smaller than it should be (and possibly lead to bad decoding)? * In the [BFV basics example in SEAL](, they show how realignment * increases * their noise budget compared to repetitive multiplication. Why is this? If we follow what the FV paper says, realignment should increase the sound and thus lower the sound budget.

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