Best Known (83, 83+11, s)-Nets in Base 9
(83, 83+11, 3355640)-Net over F9 — Constructive and digital
Digital (83, 94, 3355640)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 12, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 6, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 6, 100)-net over F81, using
- digital (71, 82, 3355440)-net over F9, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, using
- digital (7, 12, 200)-net over F9, using
(83, 83+11, 3355791)-Net in Base 9 — Constructive
(83, 94, 3355791)-net in base 9, using
- 91 times duplication [i] based on (82, 93, 3355791)-net in base 9, using
- (u, u+v)-construction [i] based on
- (6, 11, 351)-net in base 9, using
- net defined by OOA [i] based on OOA(911, 351, S9, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(911, 703, S9, 5), using
- discarding parts of the base [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(911, 703, S9, 5), using
- net defined by OOA [i] based on OOA(911, 351, S9, 5, 5), using
- digital (71, 82, 3355440)-net over F9, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, using
- (6, 11, 351)-net in base 9, using
- (u, u+v)-construction [i] based on
(83, 83+11, large)-Net over F9 — Digital
Digital (83, 94, large)-net over F9, using
- 3 times m-reduction [i] based on digital (83, 97, large)-net over F9, using
(83, 83+11, large)-Net in Base 9 — Upper bound on s
There is no (83, 94, large)-net in base 9, because
- 9 times m-reduction [i] would yield (83, 85, large)-net in base 9, but