  Electron spins in gate-defined quantum dots provide a promising platform for
quantum computation. In particular, spin-based quantum computing in gallium
arsenide takes advantage of the high quality of semiconducting materials,
reliability in fabricating arrays of quantum dots, and accurate qubit
operations. However, the effective magnetic noise arising from the hyperfine
interaction with uncontrolled nuclear spins in the host lattice constitutes a
major source of decoherence. Low frequency nuclear noise, responsible for fast
(10 ns) inhomogeneous dephasing, can be removed by echo techniques. High
frequency nuclear noise, recently studied via echo revivals, occurs in narrow
frequency bands related to differences in Larmor precession of the three
isotopes $\mathbf{^{69}Ga}$, $\mathbf{^{71}Ga}$, and $\mathbf{^{75}As}$. Here
we show that both low and high frequency nuclear noise can be filtered by
appropriate dynamical decoupling sequences, resulting in a substantial
enhancement of spin qubit coherence times. Using nuclear notch filtering, we
demonstrate a spin coherence time ($\mathbf{T_{2}}$) of 0.87 ms, five orders of
magnitude longer than typical exchange gate times, and exceeding the longest
coherence times reported to date in Si/SiGe gate-defined quantum dots.
