An Explicit Covering Array CA(411; 3, 11, 6) via Excursion-Capped Tabu Search

For integers 1 ≤ t ≤ k and v ≥ 2, the covering array number CAN(t, k, v) is the minimum number of rows N in an N × k array over v symbols such that every N × t subarray contains all vᵗ ordered t-tuples at least once. At $(t, k, v) = (3, 11, 6)$, standard tables record CAN(3, 11, 6) ≤ 420, sharpened to $418$ via PSL(2, 5) orbit seeding and tabu repair and subsequently compressed to $416$ by multi-pass post-optimization of that $418$-row array. Starting from CA(418; 3, 11, 6), iterative row deletion and single-cell repair over a transposed tuple-index table yield an explicit, row-essential covering array CA(411; 3, 11, 6) establishing CAN(3, 11, 6) ≤ 411: unweighted conflict-tabu search produces checkpoints down to $N = 412$, and two-stage WalkSAT-tabu plus excursion-capped tabu search---snapping back to the best near-covering array Abest once nuncov(A) > Eₘₐₓ---closes N = 412 → 411. We record elementary column-bonus early-abort bounds certifying exactness of the released solver's move-pruning loop and report a single-instance $24$-trial paired equal-step ablation on N = 412 → 411, where excursion-capped snap-back improves best nuncov over no-snap controls that stall early ($4/24$ vs.\ $0/24$ solved, paired McNemar $p = 0.125$) while dynamic tuple weighting provides no statistically significant benefit over unweighted snap-back.