Best Known (154, 154+12, s)-Nets in Base 3
(154, 154+12, 2796201)-Net over F3 — Constructive and digital
Digital (154, 166, 2796201)-net over F3, using
- 31 times duplication [i] based on digital (153, 165, 2796201)-net over F3, using
- net defined by OOA [i] based on linear OOA(3165, 2796201, F3, 15, 12) (dual of [(2796201, 15), 41942850, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3165, 5592403, F3, 3, 12) (dual of [(5592403, 3), 16777044, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3162, 5592402, F3, 3, 12) (dual of [(5592402, 3), 16777044, 13]-NRT-code), using
- trace code [i] based on linear OOA(981, 2796201, F9, 3, 12) (dual of [(2796201, 3), 8388522, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(981, large, F9, 12) (dual of [large, large−81, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(981, large, F9, 12) (dual of [large, large−81, 13]-code), using
- trace code [i] based on linear OOA(981, 2796201, F9, 3, 12) (dual of [(2796201, 3), 8388522, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3162, 5592402, F3, 3, 12) (dual of [(5592402, 3), 16777044, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3165, 5592403, F3, 3, 12) (dual of [(5592403, 3), 16777044, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(3165, 2796201, F3, 15, 12) (dual of [(2796201, 15), 41942850, 13]-NRT-code), using
(154, 154+12, large)-Net over F3 — Digital
Digital (154, 166, large)-net over F3, using
- 31 times duplication [i] based on digital (153, 165, large)-net over F3, using
- t-expansion [i] based on digital (151, 165, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3165, large, F3, 14) (dual of [large, large−165, 15]-code), using
- 29 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]
- 29 times code embedding in larger space [i] based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3165, large, F3, 14) (dual of [large, large−165, 15]-code), using
- t-expansion [i] based on digital (151, 165, large)-net over F3, using
(154, 154+12, large)-Net in Base 3 — Upper bound on s
There is no (154, 166, large)-net in base 3, because
- 10 times m-reduction [i] would yield (154, 156, large)-net in base 3, but