For a positive integer
N
N
, a set
B
\mathcal {B}
of integers from
{
0
,
1
,
…
,
N
−
1
}
\{0,1,\dots ,N-1\}
is called an additive
2
2
-basis for
N
N
if every integer
n
∈
{
0
,
1
,
…
,
N
−
1
}
n\in \{0,1,\dots ,N-1\}
may be represented as the sum of
2
2
elements of
B
\mathcal {B}
. We discuss the methods used to estimate the minimal size of an additive
2
2
-basis for
N
N
. We provide new examples to enrich this survey, which give good bounds. For instance, we slightly improve on the current record, from
0.46972
0.46972
to
0.46906
0.46906
.