  In this paper we present new Hadamard matrices and related combinatorial
structures. In particular, it is constructed 5202 inequivalent Hadamard
matrices of order 36 as well as 180538 Hadamard symmetric designs with 35
points in addition to those structures that admit an automorphism of order 3.
Consequently, there are at least 272116 Hadamard 3-designs with 36 points and
70 lines. We found that all Hadamard matrices constructed here are equivalent
to a regular Hadamard matrix. This fact contributes to the conjecture that
Hadamard matrices of order 36, and possibly those of order $4m^2$, are regular.
