Best Known (95, 95+10, s)-Nets in Base 3
(95, 95+10, 1677823)-Net over F3 — Constructive and digital
Digital (95, 105, 1677823)-net over F3, using
- 31 times duplication [i] based on digital (94, 104, 1677823)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 103)-net over F3, using
- digital (81, 91, 1677720)-net over F3, using
- net defined by OOA [i] based on linear OOA(391, 1677720, F3, 10, 10) (dual of [(1677720, 10), 16777109, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
- net defined by OOA [i] based on linear OOA(391, 1677720, F3, 10, 10) (dual of [(1677720, 10), 16777109, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
(95, 95+10, 4194405)-Net over F3 — Digital
Digital (95, 105, 4194405)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3105, 4194405, F3, 2, 10) (dual of [(4194405, 2), 8388705, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(314, 104, F3, 2, 5) (dual of [(104, 2), 194, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(314, 104, F3, 5) (dual of [104, 90, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(314, 146, F3, 5) (dual of [146, 132, 6]-code), using
- trace code [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(314, 146, F3, 5) (dual of [146, 132, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(314, 104, F3, 5) (dual of [104, 90, 6]-code), using
- linear OOA(391, 4194301, F3, 2, 10) (dual of [(4194301, 2), 8388511, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(391, 8388602, F3, 10) (dual of [8388602, 8388511, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- OOA 2-folding [i] based on linear OA(391, 8388602, F3, 10) (dual of [8388602, 8388511, 11]-code), using
- linear OOA(314, 104, F3, 2, 5) (dual of [(104, 2), 194, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(95, 95+10, large)-Net in Base 3 — Upper bound on s
There is no (95, 105, large)-net in base 3, because
- 8 times m-reduction [i] would yield (95, 97, large)-net in base 3, but