The covering-array nonexistence conjecture for parameters (12,8,3)(12,8,3)

A covering array CA(12,8,3)CA(12,8,3) is an array with 12 rows, 8 columns, and alphabet size 3 such that every pair of columns contains every ordered pair of symbols.

Covering-array nonexistence conjecture. A CA(12,8,3)CA(12,8,3) does not exist; consequently,

CAN(8,3)=13.CAN(8,3)=13.

The paper records the bounds 12CAN(8,3)1312\leq CAN(8,3)\leq13 and relates this conjecture to the proposed association scheme on U312\mathcal{U}^{12}_3.

Sources & referencesView supporting material

Primary source

Karen Meagher, “Covering arrays on graphs: qualitative independence graphs and extremal set partition theory”, arXiv:math/0701553 (2007).

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