Best Known (29−8, 29, s)-Nets in Base 128
(29−8, 29, 2097150)-Net over F128 — Constructive and digital
Digital (21, 29, 2097150)-net over F128, using
- net defined by OOA [i] based on linear OOA(12829, 2097150, F128, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(12829, 8388600, F128, 8) (dual of [8388600, 8388571, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12829, large, F128, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(12829, large, F128, 8) (dual of [large, large−29, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(12829, 8388600, F128, 8) (dual of [8388600, 8388571, 9]-code), using
(29−8, 29, large)-Net over F128 — Digital
Digital (21, 29, large)-net over F128, using
(29−8, 29, large)-Net in Base 128 — Upper bound on s
There is no (21, 29, large)-net in base 128, because
- 6 times m-reduction [i] would yield (21, 23, large)-net in base 128, but