Best Known (51, 51+7, s)-Nets in Base 9
(51, 51+7, 5609621)-Net over F9 — Constructive and digital
Digital (51, 58, 5609621)-net over F9, using
- net defined by OOA [i] based on linear OOA(958, 5609621, F9, 9, 7) (dual of [(5609621, 9), 50486531, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(958, 5609622, F9, 3, 7) (dual of [(5609622, 3), 16828808, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(98, 17220, F9, 3, 3) (dual of [(17220, 3), 51652, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(98, 17220, F9, 2, 3) (dual of [(17220, 2), 34432, 4]-NRT-code), using
- linear OOA(950, 5592402, F9, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
- trace code [i] based on linear OOA(8125, 2796201, F81, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- trace code [i] based on linear OOA(8125, 2796201, F81, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- linear OOA(98, 17220, F9, 3, 3) (dual of [(17220, 3), 51652, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(958, 5609622, F9, 3, 7) (dual of [(5609622, 3), 16828808, 8]-NRT-code), using
(51, 51+7, large)-Net over F9 — Digital
Digital (51, 58, large)-net over F9, using
- 94 times duplication [i] based on digital (47, 54, large)-net over F9, using
- t-expansion [i] based on digital (46, 54, large)-net over F9, using
(51, 51+7, large)-Net in Base 9 — Upper bound on s
There is no (51, 58, large)-net in base 9, because
- 5 times m-reduction [i] would yield (51, 53, large)-net in base 9, but