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**Majorization framework for balanced lattice designs.**
*(English)*
Zbl 1084.62071

Summary: This paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs, including fractional factorial designs, supersaturated designs and uniform designs. We present a general majorization framework for assessing designs, which includes a stringent criterion of majorization via pairwise coincidences and flexible surrogates via convex functions. Classical orthogonality, aberration and uniformity criteria are unified by choosing combinatorial and exponential kernels. A construction method is also sketched out.

### MSC:

62K15 | Factorial statistical designs |

### Keywords:

admissibility; discrepancy; majorization; minimum aberration; separable convex; supersaturated design; uniform design### References:

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