Best Known (139, 139+14, s)-Nets in Base 3
(139, 139+14, 1198411)-Net over F3 — Constructive and digital
Digital (139, 153, 1198411)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (10, 17, 40)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 5, 20)-net over F3, using
- net defined by OOA [i] based on linear OOA(35, 20, F3, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(35, 20, F3, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(35, 20, F3, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
- digital (5, 12, 20)-net over F3, using
- digital (2, 5, 20)-net over F3, using
- (u, u+v)-construction [i] based on
- 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 (10, 17, 40)-net over F3, using
(139, 139+14, 4194345)-Net over F3 — Digital
Digital (139, 153, 4194345)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3153, 4194345, F3, 2, 14) (dual of [(4194345, 2), 8388537, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(317, 44, F3, 2, 7) (dual of [(44, 2), 71, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(317, 88, F3, 7) (dual of [88, 71, 8]-code), using
- a “Gra†code from Grassl’s database [i]
- OOA 2-folding [i] based on linear OA(317, 88, F3, 7) (dual of [88, 71, 8]-code), using
- 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(317, 44, F3, 2, 7) (dual of [(44, 2), 71, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(139, 139+14, large)-Net in Base 3 — Upper bound on s
There is no (139, 153, large)-net in base 3, because
- 12 times m-reduction [i] would yield (139, 141, large)-net in base 3, but