On mutually orthogonal Knut Vik designs (Q1822434)

It is shown that if \(n=p_ 1^{\alpha_ 1}p_ 2^{\alpha_ 2}...p_ r^{\alpha_ r}\) is the factorization of the integer n into powers of the distinct primes \(p_ 1,p_ 2,...,p_ r\), then there exist at least N(n) mutually orthogonal Knut Vik designs of order n where \(N(n)\geq \min (p_ i-3)\), \(i=1,...,r\).