Best Known (152−14, 152, s)-Nets in Base 3
(152−14, 152, 1198405)-Net over F3 — Constructive and digital
Digital (138, 152, 1198405)-net over F3, using
- 32 times duplication [i] based on digital (136, 150, 1198405)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 14, 34)-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
- (u, u+v)-construction [i] based on
(152−14, 152, 4194342)-Net over F3 — Digital
Digital (138, 152, 4194342)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3152, 4194342, F3, 2, 14) (dual of [(4194342, 2), 8388532, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(316, 41, F3, 2, 7) (dual of [(41, 2), 66, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(316, 82, F3, 7) (dual of [82, 66, 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(316, 41, F3, 2, 7) (dual of [(41, 2), 66, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(152−14, 152, large)-Net in Base 3 — Upper bound on s
There is no (138, 152, large)-net in base 3, because
- 12 times m-reduction [i] would yield (138, 140, large)-net in base 3, but