An improved 8 × 8 approximately universal code with the large normalized diversity product

When an approximately universal code is designed with cyclic division algebras, the normalized diversity product can be intrinsically increased by a small integer non-norm element. While 2 + i has been the smallest integer non-norm element in all known 8 × 8 designs over QAM, this paper presents another new 8 × 8 code with the smaller non-norm element 1 + i over QAM.