On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes.

We give a direct construction of a (Zp×G,{0}×G,4,1) relative difference family for G∈{Z6×Z6,Z2×Z18,Z6×Z18,Z2×Z54} and every prime p≡3(mod4) with p>3. These allow us to construct an optimal (Z6m×Z6n,4,1) difference packing and an optimal (Z2m×Z18n,4,1) difference packing for every pair of positive integers (m,n). The corresponding optimal optical orthogonal signature pattern codes are also obtained. [ABSTRACT FROM AUTHOR]