Steiner systems

A Steiner system is a mathematical way of organizing elements into groups with specific intersection rules. Imagine a large set of items, and you want to create smaller groups such that every pair of items appears together in exactly one group. These systems ensure a balanced and efficient way to cover all pairs without repeats, useful in design theory, error-correcting codes, and experiment planning. Essentially, Steiner systems provide a structured approach to partitioning elements into subsets with precise intersection properties, ensuring full and uniform coverage of pairs or other combinations.