The optimal one-pass space for (1±ε)-estimating F2 in the low-error regime ε < 1/√n is Θ(n log(1/(ε^2 n))) bits.
A deterministic algorithm for sparse multivariate polynomial interpolation
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Tight Bounds for Low-Error Frequency Moment Estimation and the Power of Multiple Passes
The optimal one-pass space for (1±ε)-estimating F2 in the low-error regime ε < 1/√n is Θ(n log(1/(ε^2 n))) bits.