The table is constructed on \(\mathbb F_{11}\times\mathbb F_5^2\). Its base operation is \(i\circ j=6(i+j)\pmod{11}\). Between different fibers, the fiber output is \(t\) when \(j-i\) is a nonzero square mod 11, and \(-s-t\) otherwise. On the diagonal, fiber 0 uses the order-25 seed \(s*_0t=s+f_1(t-s)\); the other ten fibers use \(2s-t\).
The table numbers elements by \(25i+5u+v\) for \((i,(u,v))\), and each entry is the zero-based index of the product. The Paley fiber-product identities give E677; every diagonal seed is idempotent, so the whole table is idempotent and therefore satisfies E255. It is not a counterexample to E677 implying E255.
omegaestable · 2026-10-07 18:32:45