Best Known (142−20, 142, s)-Nets in Base 9
(142−20, 142, 838860)-Net over F9 — Constructive and digital
Digital (122, 142, 838860)-net over F9, using
- 95 times duplication [i] based on digital (117, 137, 838860)-net over F9, using
- net defined by OOA [i] based on linear OOA(9137, 838860, F9, 20, 20) (dual of [(838860, 20), 16777063, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(9137, 8388600, F9, 20) (dual of [8388600, 8388463, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(9137, large, F9, 20) (dual of [large, large−137, 21]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(9137, large, F9, 20) (dual of [large, large−137, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(9137, 8388600, F9, 20) (dual of [8388600, 8388463, 21]-code), using
- net defined by OOA [i] based on linear OOA(9137, 838860, F9, 20, 20) (dual of [(838860, 20), 16777063, 21]-NRT-code), using
(142−20, 142, large)-Net over F9 — Digital
Digital (122, 142, large)-net over F9, using
- 95 times duplication [i] based on digital (117, 137, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9137, large, F9, 20) (dual of [large, large−137, 21]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9137, large, F9, 20) (dual of [large, large−137, 21]-code), using
(142−20, 142, large)-Net in Base 9 — Upper bound on s
There is no (122, 142, large)-net in base 9, because
- 18 times m-reduction [i] would yield (122, 124, large)-net in base 9, but