Main result: the packing constants of Orlicz function spaces
L^{(\Phi)}[0,1]
L
(
Φ
)
[
0
,
1
]
and
L^{\Phi}[0,1]
L
Φ
[
0
,
1
]
with Luxemburg and Orlicz norm have the exact value. (i) If
F_\Phi(t)=t\varphi(t)/\Phi(t)
F
Φ
(
t
)
=
t
φ
(
t
)
/
Φ
(
t
)
is decreasing,
1<C_\Phi< 2,
1
<
C
Φ
<
2
,
then
P(L^{(\Phi)}[0,1])=P(L^{\Phi}[0,1])=\frac{2^{1/C_\Phi}}{2+2^{1/C_\Phi}};
P
(
L
(
Φ
)
[
0
,
1
]
)
=
P
(
L
Φ
[
0
,
1
]
)
=
2
1
/
C
Φ
2
+
2
1
/
C
Φ
;
(ii) If
F_\Phi(t)
F
Φ
(
t
)
is increasing,
C_\Phi> 2,
C
Φ
>
2
,
then
P(L^{(\Phi)}[0,1])=P(L^{\Phi}[0,1])=\frac{1}{1+2^{1/C_\Phi}},
P
(
L
(
Φ
)
[
0
,
1
]
)
=
P
(
L
Φ
[
0
,
1
]
)
=
1
1
+
2
1
/
C
Φ
,
where
C_\Phi=\lim\limits_{t\rightarrow\infty} F_\Phi(t)
C
Φ
=
lim
t
→
∞
F
Φ
(
t
)
.