Best Known (21, 21+4, s)-Nets in Base 8
(21, 21+4, 4194301)-Net over F8 — Constructive and digital
Digital (21, 25, 4194301)-net over F8, using
- net defined by OOA [i] based on linear OOA(825, 4194301, F8, 4, 4) (dual of [(4194301, 4), 16777179, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(825, 4194301, F8, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(825, 8388602, F8, 4) (dual of [8388602, 8388577, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(825, large, F8, 4) (dual of [large, large−25, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(825, large, F8, 4) (dual of [large, large−25, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(825, 8388602, F8, 4) (dual of [8388602, 8388577, 5]-code), using
- appending kth column [i] based on linear OOA(825, 4194301, F8, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
(21, 21+4, large)-Net over F8 — Digital
Digital (21, 25, large)-net over F8, using
- net defined by OOA [i] based on linear OOA(825, large, F8, 4, 4), using
- appending kth column [i] based on linear OOA(825, large, F8, 3, 4), using
(21, 21+4, large)-Net in Base 8 — Upper bound on s
There is no (21, 25, large)-net in base 8, because
- 2 times m-reduction [i] would yield (21, 23, large)-net in base 8, but