Best Known (30−4, 30, s)-Nets in Base 9
(30−4, 30, large)-Net over F9 — Constructive and digital
Digital (26, 30, large)-net over F9, using
- 92 times duplication [i] based on digital (24, 28, large)-net over F9, using
- net defined by OOA [i] based on linear OOA(928, large, F9, 4, 4), using
- appending kth column [i] based on linear OOA(928, large, F9, 3, 4), using
- (u, u+v)-construction [i] based on
- linear OOA(92, 10, F9, 3, 2) (dual of [(10, 3), 28, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;28,9) [i]
- linear OOA(926, 8388602, F9, 3, 4) (dual of [(8388602, 3), 25165780, 5]-NRT-code), using
- trace code [i] based on linear OOA(8113, 4194301, F81, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8113, 8388602, F81, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, large, F81, 4) (dual of [large, large−13, 5]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(8113, large, F81, 4) (dual of [large, large−13, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(8113, 8388602, F81, 4) (dual of [8388602, 8388589, 5]-code), using
- trace code [i] based on linear OOA(8113, 4194301, F81, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- linear OOA(92, 10, F9, 3, 2) (dual of [(10, 3), 28, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(928, large, F9, 3, 4), using
- net defined by OOA [i] based on linear OOA(928, large, F9, 4, 4), using
(30−4, 30, large)-Net in Base 9 — Upper bound on s
There is no (26, 30, large)-net in base 9, because
- 2 times m-reduction [i] would yield (26, 28, large)-net in base 9, but