New D-optimal designs via cyclotomy and generalised cyclotomy

  title={New D-optimal designs via cyclotomy and generalised cyclotomy},
  author={Marc Gysin},
  journal={Australasian J. Combinatorics},
  • Marc Gysin
  • Published 1997 in Australasian J. Combinatorics
D-optimal designs are n x n ±l-matrices where n == 2 mod 4 with maximum determinant. D-optimal designs obtained via circulant matrices are equivalent to 2-{ v; kl i k2 i k1 + k2 ~(v 1)} supplementary difference sets, where v = ~. We use cyclotomy to construct D-optimal designs, where v is a prime. We give a generalisation of cyclotomy and extend the cyclotomic techniques which enables use to find new D-optimal designs for composite numbers. In particular, we found, via computer-search, D… CONTINUE READING

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