Spread Construction for (36,15,6) Hadamard Difference Sets

Abstract

There are exactly 35 inequivalent (36, 15, 6) difference sets in nine groups. Eight of the nine groups have a normal Sylow 3-subgroup. We give a straightforward spread construction which explains the 32 inequivalent difference sets in these eight groups. An interesting variation on this construction provides the three difference sets in the ninth group.