For given positive integers
m
m
and
n
n
with
m
>
n
m>n
, the Prouhet–Tarry–Escott problem asks if there exist two disjoint multisets of integers of size
n
n
having identical
k
k
th moments for
1
≤
k
≤
m
1\leq k\leq m
; in the ideal case one requires
m
=
n
−
1
m=n-1
, which is maximal. We describe some searches for ideal solutions to the Prouhet–Tarry–Escott problem, especially solutions possessing a particular symmetry, both over
Z
\mathbb {Z}
and over the ring of integers of several imaginary quadratic number fields. Over
Z
\mathbb {Z}
, we significantly extend searches for symmetric ideal solutions at sizes
9
9
,
10
10
,
11
11
, and
12
12
, and we conduct extensive searches for the first time at larger sizes up to
16
16
. For the quadratic number field case, we find new ideal solutions of sizes
10
10
and
12
12
in the Gaussian integers, of size
9
9
in
Z
[
i
2
]
\mathbb {Z}[i\sqrt {2}]
, and of sizes
9
9
and
12
12
in the Eisenstein integers.