Best Known (122, 122+18, s)-Nets in Base 9
(122, 122+18, 1864134)-Net over F9 — Constructive and digital
Digital (122, 140, 1864134)-net over F9, using
- 92 times duplication [i] based on digital (120, 138, 1864134)-net over F9, using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F81, using
- net defined by OOA [i] based on linear OOA(8169, 932067, F81, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8169, large, F81, 18) (dual of [large, large−69, 19]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(8169, large, F81, 18) (dual of [large, large−69, 19]-code), using
- net defined by OOA [i] based on linear OOA(8169, 932067, F81, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- trace code for nets [i] based on digital (51, 69, 932067)-net over F81, using
(122, 122+18, large)-Net over F9 — Digital
Digital (122, 140, large)-net over F9, using
- 93 times duplication [i] based on digital (119, 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, 122+18, large)-Net in Base 9 — Upper bound on s
There is no (122, 140, large)-net in base 9, because
- 16 times m-reduction [i] would yield (122, 124, large)-net in base 9, but