Best Known (127, 127+18, s)-Nets in Base 9
(127, 127+18, 1864134)-Net over F9 — Constructive and digital
Digital (127, 145, 1864134)-net over F9, using
- 94 times duplication [i] based on digital (123, 141, 1864134)-net over F9, using
- net defined by OOA [i] based on linear OOA(9141, 1864134, F9, 21, 18) (dual of [(1864134, 21), 39146673, 19]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(9141, 5592403, F9, 3, 18) (dual of [(5592403, 3), 16777068, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(9138, 5592402, F9, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
- trace code [i] based on linear OOA(8169, 2796201, F81, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
- OOA 3-folding [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]
- OOA 3-folding [i] based on linear OA(8169, large, F81, 18) (dual of [large, large−69, 19]-code), using
- trace code [i] based on linear OOA(8169, 2796201, F81, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(9138, 5592402, F9, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(9141, 5592403, F9, 3, 18) (dual of [(5592403, 3), 16777068, 19]-NRT-code), using
- net defined by OOA [i] based on linear OOA(9141, 1864134, F9, 21, 18) (dual of [(1864134, 21), 39146673, 19]-NRT-code), using
(127, 127+18, large)-Net over F9 — Digital
Digital (127, 145, large)-net over F9, using
- t-expansion [i] based on digital (124, 145, large)-net over F9, using
(127, 127+18, large)-Net in Base 9 — Upper bound on s
There is no (127, 145, large)-net in base 9, because
- 16 times m-reduction [i] would yield (127, 129, large)-net in base 9, but