Best Known (86, 86+10, s)-Nets in Base 3
(86, 86+10, 1677724)-Net over F3 — Constructive and digital
Digital (86, 96, 1677724)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence 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
- digital (0, 5, 4)-net over F3, using
(86, 86+10, 4194305)-Net over F3 — Digital
Digital (86, 96, 4194305)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(396, 4194305, F3, 2, 10) (dual of [(4194305, 2), 8388514, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(35, 4, F3, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;3,3) [i]
- 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(35, 4, F3, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(86, 86+10, large)-Net in Base 3 — Upper bound on s
There is no (86, 96, large)-net in base 3, because
- 8 times m-reduction [i] would yield (86, 88, large)-net in base 3, but