Starting from suitable large cardinals, we force the failure of (weak) diamond at least inaccessible cardinal. The result improves an unpublished theorem Woodin and a recent Ben-Neria, Garti Hayut.

The qk (full) factorial design with replication λ is the multi-set consisting of occurrences each element q-ary vector length k; we denote this by λ×[q]k. An m×n row-column strength t an arrangement elements λ×[q]k into array (which say type Ik(m,n,q,t)) such that for row (column), set vectors therein are rows orthogonal degree k, size n (respectively, m), q levels and t. Such arrays used in ex...