Identify a deeper relationship between the weighted 2-design constructions

Identify whether a deeper relationship exists between the weighted projective 2-designs arising from Proposition 3(b) with k=1 and those arising from the Spence Sidon sets.

Background

Table 1 compares upper bounds on n(d) obtained from several constructions. The authors observe that the upper bounds from Proposition 3(b) with k=1 and from the Spence Sidon sets frequently coincide because their parameters match.

Although the numerical agreement is explained by matching parameters, the paper does not establish whether the corresponding weighted projective 2-designs or their underlying constructions are related in a deeper structural way.