Sparse 3D matrix

Certainly one way to do this would be a linked-list implementation, with the first two lists being lists of references to lists which, in the third dimension, contains the values which are populating its dimension.

You said this is sparse. You will have nodes in the list only for those points/coordinates which actually have values. You don't need to have nodes for points that don't have values. You don't have to reserve space of empty locations, the way you would for an array.

If there is no entry at all in column 2 of the second dimension, the lists for that column will all be non-existent or null.

Another thought would be a series of bitsets for each of the first two dimensions, and a list for the third dimension.

One more thought: you said you treid creating a 3D array and you ran out of space at a 256x256x256 array. Were you creating it on the heap or on the stack?