Memory and precision in noiseless Gaussian regression

For every fixed A > 0, a learner that retains at most $A{d}^2$ bits between fresh exact Gaussian linear measurements needs ${\Omega }_A(d\log (1/ϵ))$ measurements to estimate a uniformly random unit vector to angular error at most ϵ, for any $0<ϵ\le 1/10$, with probability at least 2/3. The constant is absolute for $o(d^2)$ memory.