Best Known (106−8, 106, s)-Nets in Base 3
(106−8, 106, 4194304)-Net over F3 — Constructive and digital
Digital (98, 106, 4194304)-net over F3, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 4)-net over F3, using
- digital (24, 28, 2097150)-net over F3, using
- s-reduction based on digital (24, 28, 2391485)-net over F3, using
- digital (68, 76, 2097150)-net over F3, using
- net defined by OOA [i] based on linear OOA(376, 2097150, F3, 8, 8) (dual of [(2097150, 8), 16777124, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(376, 8388600, F3, 8) (dual of [8388600, 8388524, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(376, large, F3, 8) (dual of [large, large−76, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(376, large, F3, 8) (dual of [large, large−76, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(376, 8388600, F3, 8) (dual of [8388600, 8388524, 9]-code), using
- net defined by OOA [i] based on linear OOA(376, 2097150, F3, 8, 8) (dual of [(2097150, 8), 16777124, 9]-NRT-code), using
(106−8, 106, large)-Net over F3 — Digital
Digital (98, 106, large)-net over F3, using
- 36 times duplication [i] based on digital (92, 100, large)-net over F3, using
- t-expansion [i] based on digital (91, 100, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3100, large, F3, 9) (dual of [large, large−100, 10]-code), using
- 10 times code embedding in larger space [i] based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 10 times code embedding in larger space [i] based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3100, large, F3, 9) (dual of [large, large−100, 10]-code), using
- t-expansion [i] based on digital (91, 100, large)-net over F3, using
(106−8, 106, large)-Net in Base 3 — Upper bound on s
There is no (98, 106, large)-net in base 3, because
- 6 times m-reduction [i] would yield (98, 100, large)-net in base 3, but