Best Known (129, 129+14, s)-Nets in Base 3
(129, 129+14, 1198375)-Net over F3 — Constructive and digital
Digital (129, 143, 1198375)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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 (122, 136, 1198371)-net over F3, using
- net defined by OOA [i] based on linear OOA(3136, 1198371, F3, 14, 14) (dual of [(1198371, 14), 16777058, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3136, 8388597, F3, 14) (dual of [8388597, 8388461, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3136, 8388597, F3, 14) (dual of [8388597, 8388461, 15]-code), using
- net defined by OOA [i] based on linear OOA(3136, 1198371, F3, 14, 14) (dual of [(1198371, 14), 16777058, 15]-NRT-code), using
- digital (0, 7, 4)-net over F3, using
(129, 129+14, 3204865)-Net over F3 — Digital
Digital (129, 143, 3204865)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3143, 3204865, F3, 2, 14) (dual of [(3204865, 2), 6409587, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3143, 4194305, F3, 2, 14) (dual of [(4194305, 2), 8388467, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(37, 4, F3, 2, 7) (dual of [(4, 2), 1, 8]-NRT-code), using
- dual of repetition NRT-code with length 4 [i]
- linear OOA(3136, 4194301, F3, 2, 14) (dual of [(4194301, 2), 8388466, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3136, 8388602, F3, 14) (dual of [8388602, 8388466, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- OOA 2-folding [i] based on linear OA(3136, 8388602, F3, 14) (dual of [8388602, 8388466, 15]-code), using
- linear OOA(37, 4, F3, 2, 7) (dual of [(4, 2), 1, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3143, 4194305, F3, 2, 14) (dual of [(4194305, 2), 8388467, 15]-NRT-code), using
(129, 129+14, large)-Net in Base 3 — Upper bound on s
There is no (129, 143, large)-net in base 3, because
- 12 times m-reduction [i] would yield (129, 131, large)-net in base 3, but