Best Known (84, 96, s)-Nets in Base 3
(84, 96, 88573)-Net over F3 — Constructive and digital
Digital (84, 96, 88573)-net over F3, using
- net defined by OOA [i] based on linear OOA(396, 88573, F3, 12, 12) (dual of [(88573, 12), 1062780, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(396, 531438, F3, 12) (dual of [531438, 531342, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(396, 531440, F3, 12) (dual of [531440, 531344, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(396, 531440, F3, 12) (dual of [531440, 531344, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(396, 531438, F3, 12) (dual of [531438, 531342, 13]-code), using
(84, 96, 199513)-Net over F3 — Digital
Digital (84, 96, 199513)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(396, 199513, F3, 2, 12) (dual of [(199513, 2), 398930, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(396, 265720, F3, 2, 12) (dual of [(265720, 2), 531344, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(396, 531440, F3, 12) (dual of [531440, 531344, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 2-folding [i] based on linear OA(396, 531440, F3, 12) (dual of [531440, 531344, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(396, 265720, F3, 2, 12) (dual of [(265720, 2), 531344, 13]-NRT-code), using
(84, 96, large)-Net in Base 3 — Upper bound on s
There is no (84, 96, large)-net in base 3, because
- 10 times m-reduction [i] would yield (84, 86, large)-net in base 3, but