Definition: Admissible stencil

For $0<\delta \le 1/2$ and $L\ge 4\sqrt{D}/\delta$, a $(\delta ,L)$-stencil is a finite set $S\subset {\mathbb{Z}}^D\setminus \{0\}$ such that:

1. $S=-S$ and $S$ contains $\pm e_i$;

2. $\Vert s{\Vert }_2\le L$ for every $s\in S$;

3. directions of generators with $\Vert s{\Vert }_2\ge (1-\delta )L$ form a $\delta$-net of the unit sphere.