Best Known (122, 141, s)-Nets in Base 9
(122, 141, 932094)-Net over F9 — Constructive and digital
Digital (122, 141, 932094)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 12, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (110, 129, 932066)-net over F9, using
- net defined by OOA [i] based on linear OOA(9129, 932066, F9, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9129, 8388595, F9, 19) (dual of [8388595, 8388466, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9129, large, F9, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 916−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(9129, large, F9, 19) (dual of [large, large−129, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9129, 8388595, F9, 19) (dual of [8388595, 8388466, 20]-code), using
- net defined by OOA [i] based on linear OOA(9129, 932066, F9, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
- digital (3, 12, 28)-net over F9, using
(122, 141, large)-Net over F9 — Digital
Digital (122, 141, large)-net over F9, using
- 94 times duplication [i] based on digital (118, 137, large)-net over F9, using
- t-expansion [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
- t-expansion [i] based on digital (117, 137, large)-net over F9, using
(122, 141, large)-Net in Base 9 — Upper bound on s
There is no (122, 141, large)-net in base 9, because
- 17 times m-reduction [i] would yield (122, 124, large)-net in base 9, but