On Full Orthogonal Designs in Order $72$

Abstract

We find new full orthogonal designs in order 72 and show that of 2700 possible $OD(72;s_1,s_2,s_3,72–s_1–s_2–s_3)$, 335 are known, of 432 possible $OD(72;s_1,s_2,72–s_1–s_2)$, 308 are known. All possible $OD(72;s_1,72–s_1)$ are known.