“…But for the case H ∈ (0, 1 2 ) (called as "rough noise"), the existing discussions seem to be few. In [10], the authors propose numerical analyses about the second-order stochastic differential equation driven by spatial fractional Gaussian noise with H ∈ (0, 1 2 ); the reference [23] uses the equivalence of different fractional Sobolev spaces and the assumption τ < τ * (τ * depends on the spatial discretization) to provide a unified strong convergence analysis for fractional stochastic partial differential equation driven by fractional cylinder noise with H ∈ (0, 1); in [9], the authors propose the regularity estimates and the corresponding numerical analyses about the stochastic evolution equation driven by fractional Brownian sheet with H 1 ∈ (0, 1 2 ) and H 2 = 1 2 . In this paper, we focus on the fractional diffusion equation driven by fractional Brownian sheet with Hurst parameters H 1 , H 2 ∈ (0, 1 2 ] numerically, which are both rough in the temporal and spatial directions.…”