Best Known (21, 21+4, s)-Nets in Base 9
(21, 21+4, 4194301)-Net over F9 — Constructive and digital
Digital (21, 25, 4194301)-net over F9, using
- net defined by OOA [i] based on linear OOA(925, 4194301, F9, 4, 4) (dual of [(4194301, 4), 16777179, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(925, 4194301, F9, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(925, 8388602, F9, 4) (dual of [8388602, 8388577, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(925, large, F9, 4) (dual of [large, large−25, 5]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(925, large, F9, 4) (dual of [large, large−25, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(925, 8388602, F9, 4) (dual of [8388602, 8388577, 5]-code), using
- appending kth column [i] based on linear OOA(925, 4194301, F9, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
(21, 21+4, large)-Net over F9 — Digital
Digital (21, 25, large)-net over F9, using
- 91 times duplication [i] based on digital (20, 24, large)-net over F9, using
- net defined by OOA [i] based on linear OOA(924, large, F9, 4, 4), using
- appending kth column [i] based on linear OOA(924, large, F9, 3, 4), using
- net defined by OOA [i] based on linear OOA(924, large, F9, 4, 4), using
(21, 21+4, large)-Net in Base 9 — Upper bound on s
There is no (21, 25, large)-net in base 9, because
- 2 times m-reduction [i] would yield (21, 23, large)-net in base 9, but