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Judging by practical experience, solving classification problems for combinatorial objects such as codes and designs is a computationally demanding task. A question of a different nature is what can be said from the perspective of computational complexity theory, where it is common to regard a computational problem tractable only if it admits a polynomially resource-bounded algorithm, whereas problems for which no such algorithm exists are regarded as intractable.

There is not a more appropriate conclusion of a book on classification methods for designs than a discussion of the nonexistence of projective planes of order 10. Not only is this one of the main achievements on this topic – probably, main – but it also illustrates how a variety of combinatorial results and ideas combined with extensive computations lead to a solution of this problem. Interestingly, codes, the other main type of objects considered in this book, play a central role in the approach.