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Values of minors of an infinite family of D-optimal designs and their application to the growth problem: II

Journal Article


Abstract


  • We obtain explicit formulae for the values of the 2v - j minors, j = 0,1,2, of Doptimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of 2 - {s2 + s + 1; s(s-1)/2, s(s+1)/2; s(s-1)/2} supplementary difference sets (SDS). This allows us to obtain information on the growth problem for families of matrices which have moderately large growth. Some of our theoretical formulae suggest that growth greater than 2v may occur, but experimentation has not yet supported this result. An open problem remains to establish whether the (1, -1) completely pivoted (CP) incidence matrices of 2 - {s2 + s+1; s(s-1)/2, s(s+1)/2; s(s-1)/2} SDS, which yield D-optimal designs, can have growth greater than 2v.

Publication Date


  • 2003

Citation


  • Koukouvinos, C., Mitrouli, M., & Seberry, J. (2003). Values of minors of an infinite family of D-optimal designs and their application to the growth problem: II. SIAM Journal on Matrix Analysis and Applications, 24(3), 715-727. doi:10.1137/S0895479801386845

Scopus Eid


  • 2-s2.0-0041914123

Web Of Science Accession Number


Start Page


  • 715

End Page


  • 727

Volume


  • 24

Issue


  • 3

Abstract


  • We obtain explicit formulae for the values of the 2v - j minors, j = 0,1,2, of Doptimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of 2 - {s2 + s + 1; s(s-1)/2, s(s+1)/2; s(s-1)/2} supplementary difference sets (SDS). This allows us to obtain information on the growth problem for families of matrices which have moderately large growth. Some of our theoretical formulae suggest that growth greater than 2v may occur, but experimentation has not yet supported this result. An open problem remains to establish whether the (1, -1) completely pivoted (CP) incidence matrices of 2 - {s2 + s+1; s(s-1)/2, s(s+1)/2; s(s-1)/2} SDS, which yield D-optimal designs, can have growth greater than 2v.

Publication Date


  • 2003

Citation


  • Koukouvinos, C., Mitrouli, M., & Seberry, J. (2003). Values of minors of an infinite family of D-optimal designs and their application to the growth problem: II. SIAM Journal on Matrix Analysis and Applications, 24(3), 715-727. doi:10.1137/S0895479801386845

Scopus Eid


  • 2-s2.0-0041914123

Web Of Science Accession Number


Start Page


  • 715

End Page


  • 727

Volume


  • 24

Issue


  • 3