An efficient mixed deterministic and sparse-stochastic plane-wave approach is developed for periodic generalized-Kohn-Sham density functional theory band-structure calculations with extensive $k$-point sampling, for any hybrid-exchange density functional. The method works for very large elementary cells over many $k$ points, and we benchmark it on covalently bonded solids and molecular crystals with nonbonded interactions, for systems of up to 33 000 atoms. Memory and CPU requirements scale quasilinearly with the number of atoms.

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• Electronic structure
• Crystal structures
• Diamond
• Insulators
• Semiconductors
• Wide band gap systems
• Density functional calculations
• Density functional theory
• Density functional theory development
• Hybrid functionals
• Pseudopotentials