In terms of the minimal
N
N
-point diameter
D
d
(
N
)
D_d(N)
for
R
d
,
\mathbb {R}^d,
we determine, for a class of continuous real-valued functions
f
f
on
[
0
,
+
∞
]
,
[0,+\infty ],
the
N
N
-point
f
f
-best-packing constant
min
{
f
(
‖
x
−
y
‖
)
:
x
,
y
∈
R
d
}
\min \{f(\|x-y\|)\, :\, x,y\in \mathbb {R}^d\}
, where the minimum is taken over point sets of cardinality
N
.
N.
We also show that
\[
N
1
/
d
Δ
d
−
1
/
d
−
2
≤
D
d
(
N
)
≤
N
1
/
d
Δ
d
−
1
/
d
,
N
≥
2
,
N^{1/d}\Delta _d^{-1/d}-2\le D_d(N)\le N^{1/d}\Delta _d^{-1/d}, \quad N\ge 2,
\]
where
Δ
d
\Delta _d
is the maximal sphere packing density in
R
d
\mathbb {R}^d
. Further, we provide asymptotic estimates for the
f
f
-best-packing constants as
N
→
∞
N\to \infty
.