Best Known (135, 135+14, s)-Nets in Base 3
(135, 135+14, 1198397)-Net over F3 — Constructive and digital
Digital (135, 149, 1198397)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 13, 26)-net 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
(135, 135+14, 4194327)-Net over F3 — Digital
Digital (135, 149, 4194327)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3149, 4194327, F3, 2, 14) (dual of [(4194327, 2), 8388505, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(313, 26, F3, 2, 7) (dual of [(26, 2), 39, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 13, 26)-net over F3, 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(313, 26, F3, 2, 7) (dual of [(26, 2), 39, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(135, 135+14, large)-Net in Base 3 — Upper bound on s
There is no (135, 149, large)-net in base 3, because
- 12 times m-reduction [i] would yield (135, 137, large)-net in base 3, but