Conjecture on the affine full-dimensionality of D-optimal factorial designs

Let rr denote the number of runs, and distinguish affinely full-dimensional factorial designs from subset fractional factorial designs. The D-optimal design conjecture. The DD-optimal design is affinely full-dimensional factorial when

r5,6,7(mod8),r\equiv 5,6,7\pmod{8},

and it is subset fractional factorial when

r0,1,2,3,4(mod8).r\equiv 0,1,2,3,4\pmod{8}.

The conjecture records the periodicity observed in the table of known maximal determinants and predicts the type of DD-optimal design according to rr modulo 88. The source gives no resolution or status evidence.

Sources & referencesView supporting material

Primary source

Satoshi Aoki and Akimichi Takemura, “Some characterizations of affinely full-dimensional factorial designs”, arXiv:0812.0196 (2008).

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