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flyback & boost applications

For flyback & boost applications, powder cores such as Kool-mu, Xmu, etc... are usually best performing and lowest cost. Even these may need to be gapped and if CCM operation is required, a "stepped-gap" is preferred to allow a large load compliance. Center stepped gaps reduce the fringe flux greatly as there is never a complete gap, only localized saturation. This permits the inductor's value to "swing" more and accommodate the required operation.
With only the center leg with a gap, the outer copper band can be applied without significant loss.

To explore further, dissimilar core materials can be used in parallel, ferrite & powdered types, such that different materials provide function at different operating points within the same construction. Some decades ago, we had some high power projects that utilized fixed magnets within a ferrite's gap to provide a flux bias offset for a forward topology.

Abe Pressman wasn't big on exploring magnetic losses, however he operated at lower frequencies than are typical today. MPPs are great with large DC bias, but suffer high loss if AC swing is large and fast. Toroids also have the least efficient winding window, however, they are best to mitigate emi.

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