Best Known (92, 114, s)-Nets in Base 9
(92, 114, 5404)-Net over F9 — Constructive and digital
Digital (92, 114, 5404)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 18, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- digital (74, 96, 5368)-net over F9, using
- net defined by OOA [i] based on linear OOA(996, 5368, F9, 22, 22) (dual of [(5368, 22), 118000, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(996, 59048, F9, 22) (dual of [59048, 58952, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(996, 59048, F9, 22) (dual of [59048, 58952, 23]-code), using
- net defined by OOA [i] based on linear OOA(996, 5368, F9, 22, 22) (dual of [(5368, 22), 118000, 23]-NRT-code), using
- digital (7, 18, 36)-net over F9, using
(92, 114, 5406)-Net in Base 9 — Constructive
(92, 114, 5406)-net in base 9, using
- (u, u+v)-construction [i] based on
- (7, 18, 38)-net in base 9, using
- base change [i] based on digital (1, 12, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- base change [i] based on digital (1, 12, 38)-net over F27, using
- digital (74, 96, 5368)-net over F9, using
- net defined by OOA [i] based on linear OOA(996, 5368, F9, 22, 22) (dual of [(5368, 22), 118000, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(996, 59048, F9, 22) (dual of [59048, 58952, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(996, 59048, F9, 22) (dual of [59048, 58952, 23]-code), using
- net defined by OOA [i] based on linear OOA(996, 5368, F9, 22, 22) (dual of [(5368, 22), 118000, 23]-NRT-code), using
- (7, 18, 38)-net in base 9, using
(92, 114, 164287)-Net over F9 — Digital
Digital (92, 114, 164287)-net over F9, using
(92, 114, large)-Net in Base 9 — Upper bound on s
There is no (92, 114, large)-net in base 9, because
- 20 times m-reduction [i] would yield (92, 94, large)-net in base 9, but