Combinatorial design

These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella.

Modern applications are also found in a wide gamut of areas including finite geometry, tournament scheduling, lotteries, mathematical chemistry, mathematical biology, algorithm design and analysis, networking, group testing and cryptography.

It has been further shown that if a solution exists for q congruent to 1 or 2 mod 4, then q is a sum of two square numbers.

This last result, the Bruck–Ryser theorem, is proved by a combination of constructive methods based on finite fields and an application of quadratic forms.

One of the earliest datable application of combinatorial design is found in India in the book Brhat Samhita by Varahamihira, written around 587 AD, for the purpose of making perfumes using 4 substances selected from 16 different substances using a magic square.