Best Known (76, 76+10, s)-Nets in Base 9
(76, 76+10, 3355640)-Net over F9 — Constructive and digital
Digital (76, 86, 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 (64, 74, 3355440)-net over F9, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- digital (7, 12, 200)-net over F9, using
(76, 76+10, 3355791)-Net in Base 9 — Constructive
(76, 86, 3355791)-net in base 9, using
- 91 times duplication [i] based on (75, 85, 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 (64, 74, 3355440)-net over F9, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- (6, 11, 351)-net in base 9, using
- (u, u+v)-construction [i] based on
(76, 76+10, large)-Net over F9 — Digital
Digital (76, 86, large)-net over F9, using
- 3 times m-reduction [i] based on digital (76, 89, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(989, large, F9, 13) (dual of [large, large−89, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(989, large, F9, 13) (dual of [large, large−89, 14]-code), using
(76, 76+10, large)-Net in Base 9 — Upper bound on s
There is no (76, 86, large)-net in base 9, because
- 8 times m-reduction [i] would yield (76, 78, large)-net in base 9, but