Best Known (26, 32, s)-Nets in Base 3
(26, 32, 2187)-Net over F3 — Constructive and digital
Digital (26, 32, 2187)-net over F3, using
- net defined by OOA [i] based on linear OOA(332, 2187, F3, 6, 6) (dual of [(2187, 6), 13090, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(332, 2187, F3, 5, 6) (dual of [(2187, 5), 10903, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(332, 6561, F3, 6) (dual of [6561, 6529, 7]-code), using
- 1 times truncation [i] based on linear OA(333, 6562, F3, 7) (dual of [6562, 6529, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(333, 6562, F3, 7) (dual of [6562, 6529, 8]-code), using
- OA 3-folding and stacking [i] based on linear OA(332, 6561, F3, 6) (dual of [6561, 6529, 7]-code), using
- appending kth column [i] based on linear OOA(332, 2187, F3, 5, 6) (dual of [(2187, 5), 10903, 7]-NRT-code), using
(26, 32, 5514)-Net over F3 — Digital
Digital (26, 32, 5514)-net over F3, using
- net defined by OOA [i] based on linear OOA(332, 5514, F3, 6, 6) (dual of [(5514, 6), 33052, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(332, 5514, F3, 5, 6) (dual of [(5514, 5), 27538, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(332, 5514, F3, 6) (dual of [5514, 5482, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(332, 6561, F3, 6) (dual of [6561, 6529, 7]-code), using
- 1 times truncation [i] based on linear OA(333, 6562, F3, 7) (dual of [6562, 6529, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(333, 6562, F3, 7) (dual of [6562, 6529, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(332, 6561, F3, 6) (dual of [6561, 6529, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(332, 5514, F3, 6) (dual of [5514, 5482, 7]-code), using
- appending kth column [i] based on linear OOA(332, 5514, F3, 5, 6) (dual of [(5514, 5), 27538, 7]-NRT-code), using
(26, 32, 111593)-Net in Base 3 — Upper bound on s
There is no (26, 32, 111594)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1853 064168 475185 > 332 [i]