Best Known (119, 119+28, s)-Nets in Base 9
(119, 119+28, 37960)-Net over F9 — Constructive and digital
Digital (119, 147, 37960)-net over F9, using
- 92 times duplication [i] based on digital (117, 145, 37960)-net over F9, using
- net defined by OOA [i] based on linear OOA(9145, 37960, F9, 28, 28) (dual of [(37960, 28), 1062735, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(9145, 531440, F9, 28) (dual of [531440, 531295, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9145, 531441, F9, 28) (dual of [531441, 531296, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(9145, 531441, F9, 28) (dual of [531441, 531296, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(9145, 531440, F9, 28) (dual of [531440, 531295, 29]-code), using
- net defined by OOA [i] based on linear OOA(9145, 37960, F9, 28, 28) (dual of [(37960, 28), 1062735, 29]-NRT-code), using
(119, 119+28, 301037)-Net over F9 — Digital
Digital (119, 147, 301037)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9147, 301037, F9, 28) (dual of [301037, 300890, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9147, 531451, F9, 28) (dual of [531451, 531304, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(9145, 531441, F9, 28) (dual of [531441, 531296, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(9133, 531441, F9, 25) (dual of [531441, 531308, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(9147, 531451, F9, 28) (dual of [531451, 531304, 29]-code), using
(119, 119+28, large)-Net in Base 9 — Upper bound on s
There is no (119, 147, large)-net in base 9, because
- 26 times m-reduction [i] would yield (119, 121, large)-net in base 9, but