Random Grouping of arrays based on average values in R

I have a data frame given below. The first column is for the IDs of a list of measured values given in the second column. I would like to group IDs ( 8 in each group) into 3 groups randomly many times until the differences between the group Value means would be the smallest, i.e. an ANOVA analysis of the final group means would give a p-value of close to 1.0.

ID Value
01F 128.1
02F 196.5
03F 118.3
04F 165.5
05F 105.0
06F 187.5
07F 105.5
08F 148.6
09F 147.2
10F 110.9
11F 109.9
12F 136.5
13F 105.4
14F 196.3
15F 199.2
18F 174.8
19F 138.9
21F 128.1
22F 196.5
26F 187.5
27F 105.5
28F 148.6
29F 147.2
30F 110.9

Thank you.