I assume you mean extra low frequency, say 60 kHz?

First chose a ferrite that has good permeability at the frequency of operation. Then look up when it saturates. You need to choose a maximum reactive power (or current) for your design, then you can determine the core area. Next choose the type of core, E, UI etc. and depending on the application whether you need a gapped core. Choice here is determined by the "use" of the inductor. is it a filter, or tank coil etc. Then look up the ferrite characteristics at your operating conditions. From this you can derive the number of turns for a given inductance and wire size for a given current. You may need to iterate around wire diameter and core size to get the best design. (for example, you may need a bigger core to get all the turns in place)

Higher operating voltages will require better (usually thicker) insulation and so will increase core size above the minimum needed to prevent saturation.

Hope this helps.

regards

Dr. Paul

thank you sir for nice response 

Close to what Paul Howard says: "Inductors and transformers for power electronics"   ISBN: 1574446797    Chapter 2 In fig. 2.2  saturation limited design.

For extra low frequency below 1000Hz, one usually has an adavantage to take iron instead of ferrite, as the saturation induction is higher. Tyipically 0.3mm iron sheets, but down to 0.1mm exist.

Up to 20 kHz, amorphous iron cut core can be an optimal choice. The ribbon thickness is 20µm.

From 5kHz on one better checks the losses due to eddy current losses (also chapter 2 or 5), and possible circulating currents if some wires are put in parallel.

Nanocrystalline iron (processed amorphous) has even lower losses than ferrite and allows a higher induction, but it is usually not available in cut cores, and costs more.

The question is also what sizing and if an almost optimal core is desired.

Dr Paul and Alex has given very good insight. For ELF, if you need higher inductance (order of Henry), it is very difficult to get suitable core size as no of turns increase due to non availability of higher AL valued core. Hence E & I core to be used. Alternatively you can go for R core, especially, if current flow is very high (This is to avoid saturation)