A PL~sphere is called a seed if it is not obtained by simplicial wedge operation, which preserves Buchstaber numbers.

For a seed of dimension $n-1$ with $n+p$ vertices, Choi and Park proved that the inequality $n+p \leq 2^{p} - 1$ holds if $p \geq 3$, and as a corollary, the number of seeds is finite for each fixed number $p$.

We introduce a method to generate a new seed from an original seed as preserving its Buchstaber number, and apply to show that for all integers $n \geq 2$, $p \geq 3$ satisfying the inequality, there exists a seed of dimension $n-1$ with $n+p$ vertices whose Buchstaber number is maximal, particularly, the inequality is tight.

This is joint work with Suyoung Choi.