Best Known (127, 127+19, s)-Nets in Base 9
(127, 127+19, 1864133)-Net over F9 — Constructive and digital
Digital (127, 146, 1864133)-net over F9, using
- net defined by OOA [i] based on linear OOA(9146, 1864133, F9, 21, 19) (dual of [(1864133, 21), 39146647, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(9146, 5592400, F9, 3, 19) (dual of [(5592400, 3), 16777054, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9146, 5592402, F9, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- trace code [i] based on linear OOA(8173, 2796201, F81, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8173, large, F81, 19) (dual of [large, large−73, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8173, large, F81, 19) (dual of [large, large−73, 20]-code), using
- trace code [i] based on linear OOA(8173, 2796201, F81, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9146, 5592402, F9, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(9146, 5592400, F9, 3, 19) (dual of [(5592400, 3), 16777054, 20]-NRT-code), using
(127, 127+19, large)-Net over F9 — Digital
Digital (127, 146, large)-net over F9, using
- 91 times duplication [i] based on digital (126, 145, large)-net over F9, using
- t-expansion [i] based on digital (124, 145, large)-net over F9, using
(127, 127+19, large)-Net in Base 9 — Upper bound on s
There is no (127, 146, large)-net in base 9, because
- 17 times m-reduction [i] would yield (127, 129, large)-net in base 9, but