conference matrices

[Joerg Arndt]

Why is sequence A000952 restricted to 2 mod 4?

For the record:

---- snip ----
The conference matrices obtained are of size $c=q^n+1$ where $q$ is an odd prime.
The values $c\leq{}100$ are:
    4, 6, 8, 10, 12, 14, 18, 20, 24, 26, 28, 30, 32, 38, 42, 44, 48,
    50, 54, 60, 62, 68, 72, 74, 80, 82, 84, 90, 98
---- snip ----
(cd. A061344)
and
---- snip ----
We do not obtain conference matrices for any odd $c$ and these even
values $c\leq{}100$:
    2, 16, 22, 34, 36, 40, 46, 52, 56, 58, 64, 66, 70, 76, 78, 86, 88, 92, 94, 96, 100
For example, $c=16=15+1=3\cdot{}5+1$ has not the required form.
---- snip ----

regards,   jj