  We study the connection between mutually unbiased bases and mutually
orthogonal extraordinary supersquares, a wider class of squares which does not
contain only the Latin squares. We show that there are four types of complete
sets of mutually orthogonal extraordinary supersquares for the dimension $d=8$.
We introduce the concept of physical striation and show that this is equivalent
to the extraordinary supersquare. The general algorithm for obtaining the
mutually unbiased bases and the physical striations is constructed and it is
shown that the complete set of mutually unbiased physical striations is
equivalent to the complete set of mutually orthogonal extraordinary
supersquares. We apply the algorithm to two examples: one for two-qubit systems
($d=4$) and one for three-qubit systems ($d=8$), by using the Type II complete
sets of mutually orthogonal extraordinary supersquares of order 8.
