Block-Wise Construction of Trimagic Squares with Bimagic Blocks of Order 8 (16384)

A balanced complementary product is specialized to a fixed normal bimagic square of order eight. Given a normal trimagic outer square of order m divisible by four, the construction produces a normal trimagic square of order 8m. Every aligned 8x8 block is bimagic but not trimagic, and the ordinary magic constants of the blocks are pairwise distinct. We give an explicit periodic sign pattern, prove the required cancellation on rows, columns and both principal diagonals, and derive the block constants and an exact obstruction for a bimagic outer square. The retained computational record comprises ten orders from 96 to 16\,384, including 768, 1024 and 1536. Numerical inventories and checksums distinguish the recorded matrices from other squares of the same orders. The contribution is a documented specialization and computational study of complementary products, rather than a claim of a new general product theorem. Text files of complete work are attached