On Generating and Classifying All QN-M Regular Designs for Square-Free Q
By extending results developed for q a prime or a prime power we develop methods for generating all q n-m regular designs for q a product of distinct primes, along with their confounded interactions or defining contrasts. The method of generation produces a unique and decodable number for each such design and explicit formulae are supplied for each step of the coding and decoding algorithm. The case where q is a product of two separate primes is studied in detail, with indications given for extensions to more primes and different values of q for each factor, this latter case covering in particular the situation where each q is a single, possibly distinct, prime.
KeywordsFractional factorials block designs complete sub-spaces algorithms design numbers confounded interactions resolution numbers aberration
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