Best Known (119−19, 119, s)-Nets in Base 9
(119−19, 119, 531444)-Net over F9 — Constructive and digital
Digital (100, 119, 531444)-net over F9, using
- net defined by OOA [i] based on linear OOA(9119, 531444, F9, 19, 19) (dual of [(531444, 19), 10097317, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9119, 4782997, F9, 19) (dual of [4782997, 4782878, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9119, 4783003, F9, 19) (dual of [4783003, 4782884, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(96, 34, F9, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(9119, 4783003, F9, 19) (dual of [4783003, 4782884, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9119, 4782997, F9, 19) (dual of [4782997, 4782878, 20]-code), using
(119−19, 119, 3770681)-Net over F9 — Digital
Digital (100, 119, 3770681)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9119, 3770681, F9, 19) (dual of [3770681, 3770562, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9119, 4783003, F9, 19) (dual of [4783003, 4782884, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(96, 34, F9, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(9119, 4783003, F9, 19) (dual of [4783003, 4782884, 20]-code), using
(119−19, 119, large)-Net in Base 9 — Upper bound on s
There is no (100, 119, large)-net in base 9, because
- 17 times m-reduction [i] would yield (100, 102, large)-net in base 9, but