> dat
   num_bloc F      E      y
1     bloc1 T      B 0.0695
2     bloc2 T      B 0.1540
3     bloc3 T      B 0.0634
4     bloc1 C      B 0.0770
5     bloc2 C      B 0.0746
6     bloc3 C      B 0.1020
7     bloc1 P      B 0.0825
8     bloc2 P      B 0.0559
9     bloc3 P      B 0.0832
10    bloc1 T   B.Br 0.0891
11    bloc2 T   B.Br 0.1050
12    bloc3 T   B.Br 0.1150
13    bloc1 C   B.Br 0.1580
14    bloc2 C   B.Br 0.0989
15    bloc3 C   B.Br 0.1510
16    bloc1 P   B.Br 0.1020
17    bloc2 P   B.Br 0.0751
18    bloc3 P   B.Br 0.0655
19    bloc1 T    B.S 0.1020
20    bloc2 T    B.S 0.0755
21    bloc3 T    B.S 0.0631
22    bloc1 C    B.S 0.0705
23    bloc2 C    B.S 0.0782
24    bloc3 C    B.S 0.0751
25    bloc1 P    B.S 0.0826
26    bloc2 P    B.S 0.0800
27    bloc3 P    B.S 0.0996
28    bloc1 T B.S.Br 0.0850
29    bloc2 T B.S.Br 0.0688
30    bloc3 T B.S.Br 0.0727
31    bloc1 C B.S.Br 0.0762
32    bloc2 C B.S.Br 0.0880
33    bloc3 C B.S.Br 0.0751
34    bloc1 P B.S.Br 0.0694
35    bloc2 P B.S.Br 0.0619
36    bloc3 P B.S.Br 0.0627
>

full0 <- lme(y~F*E,control=lmeControl(opt = "optim"),
                                random=~1|num_bloc/E,data=dat,method='ML',
                                contrasts = list(F='contr.treatment'),na.action="na.exclude")

full <- update(full0,weight=varIdent(form = ~ 1 | E*F))

main0 <- lme(y~F+E,control=lmeControl(opt = "optim"),
                                random=~1|num_bloc/E,data=dat,method='ML',
                                contrasts = list(F='contr.treatment'),na.action="na.exclude")
main <- update(main0,weight=varIdent(form = ~ 1 | E*F))

anova(full,main)
     Model df       AIC       BIC   logLik   Test  L.Ratio p-value
full     1 26 -174.1895 -133.0180 113.0948
main     2 20 -175.5688 -143.8985 107.7844 1 vs 2 10.62064  0.1008

> contrast(emmeans(full0,~F),method="trt.vs.ctrl")
NOTE: Results may be misleading due to involvement in interactions
 contrast estimate      SE df t.ratio p.value
 C - T     0.00513 0.00856 16  0.599  0.7690
 P - T    -0.01189 0.00856 16 -1.390  0.3123

Results are averaged over the levels of: E
P value adjustment: dunnettx method for 2 tests

> contrast(emmeans(full,~F),method="trt.vs.ctrl")
NOTE: Results may be misleading due to involvement in interactions
 contrast estimate      SE df t.ratio p.value
 C - T     0.00513 0.00973 16  0.527  0.8110
 P - T    -0.01189 0.00905 16 -1.314  0.3482

Results are averaged over the levels of: E
P value adjustment: dunnettx method for 2 tests

> contrast(emmeans(main0,~F),method="trt.vs.ctrl")
 contrast estimate      SE df t.ratio p.value
 C - T     0.00513 0.00902 22  0.568  0.7857
 P - T    -0.01189 0.00902 22 -1.318  0.3392

Results are averaged over the levels of: E
P value adjustment: dunnettx method for 2 tests

> contrast(emmeans(main,~F),method="trt.vs.ctrl")
 contrast  estimate      SE df t.ratio p.value
 C - T     0.000686 0.00469 22  0.146  0.9773
 P - T    -0.011254 0.00222 22 -5.072  0.0001

Results are averaged over the levels of: E
P value adjustment: dunnettx method for 2 tests