Best Known (41−3, 41, s)-Nets in Base 9
(41−3, 41, large)-Net over F9 — Constructive and digital
Digital (38, 41, large)-net over F9, using
- 93 times duplication [i] based on digital (35, 38, large)-net over F9, using
- t-expansion [i] based on digital (33, 38, large)-net over F9, using
- trace code for nets [i] based on digital (14, 19, 4194383)-net over F81, using
- net defined by OOA [i] based on linear OOA(8119, 4194383, F81, 5, 5) (dual of [(4194383, 5), 20971896, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(8119, 4194383, F81, 4, 5) (dual of [(4194383, 4), 16777513, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(812, 82, F81, 4, 2) (dual of [(82, 4), 326, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;326,81) [i]
- linear OOA(8117, 4194301, F81, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8117, large, F81, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(8117, large, F81, 5) (dual of [large, large−17, 6]-code), using
- linear OOA(812, 82, F81, 4, 2) (dual of [(82, 4), 326, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(8119, 4194383, F81, 4, 5) (dual of [(4194383, 4), 16777513, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8119, 4194383, F81, 5, 5) (dual of [(4194383, 5), 20971896, 6]-NRT-code), using
- trace code for nets [i] based on digital (14, 19, 4194383)-net over F81, using
- t-expansion [i] based on digital (33, 38, large)-net over F9, using
(41−3, 41, large)-Net in Base 9 — Upper bound on s
There is no (38, 41, large)-net in base 9, because
- 1 times m-reduction [i] would yield (38, 40, large)-net in base 9, but