On Full Orthogonal Designs in Order \(56\)

Abstract

We find new full orthogonal designs in order \(56\) and show that of
\(1285\) possible \(OD(56; s_1, s_2, s_3,56 – s_1 – s_2 – s_3)\) \(163\) are known, of
\(261\) possible \(OD(56; s_1, s_2, 56 – s_1 – s_2)\) \(179\) are known. All possible
\(OD(56; s_1,56 – s_1)\) are known.