algorithm - Find the maximum hyperrectangle contained in a set of points -

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i have question similar 1 ( find largest rectangular block satisfying condition without iterating explicitly). in case have multidimensional (up 6 dimensions) binary array , want find largest hyperrectangle (by volume, i.e. product of dimensions) contains 1's.

for example, in 3d, data like:

data = table[if[i - j - k <= -1, 1, 0]    , {i, 11}    , {j, 11}    , {k, 11}    ];

http://i.imgur.com/brgiuoq.jpg

enter image description here

note i'm looking algorithm, , doesn't have written in mathematica.


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