Best Known (150, 164, s)-Nets in Base 3
(150, 164, 1198735)-Net over F3 — Constructive and digital
Digital (150, 164, 1198735)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (21, 28, 364)-net over F3, using
- net defined by OOA [i] based on linear OOA(328, 364, F3, 7, 7) (dual of [(364, 7), 2520, 8]-NRT-code), 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 (21, 28, 364)-net over F3, using
(150, 164, 8002540)-Net over F3 — Digital
Digital (150, 164, 8002540)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3164, 8002540, F3, 14) (dual of [8002540, 8002376, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3164, large, F3, 14) (dual of [large, large−164, 15]-code), using
- 28 times code embedding in larger space [i] 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]
- 28 times code embedding in larger space [i] based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3164, large, F3, 14) (dual of [large, large−164, 15]-code), using
(150, 164, large)-Net in Base 3 — Upper bound on s
There is no (150, 164, large)-net in base 3, because
- 12 times m-reduction [i] would yield (150, 152, large)-net in base 3, but