Best Known (118, 140, s)-Nets in Base 9
(118, 140, 434818)-Net over F9 — Constructive and digital
Digital (118, 140, 434818)-net over F9, using
- net defined by OOA [i] based on linear OOA(9140, 434818, F9, 22, 22) (dual of [(434818, 22), 9565856, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9140, 4782998, F9, 22) (dual of [4782998, 4782858, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9140, 4783003, F9, 22) (dual of [4783003, 4782863, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(9134, 4782969, F9, 22) (dual of [4782969, 4782835, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(9140, 4783003, F9, 22) (dual of [4783003, 4782863, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(9140, 4782998, F9, 22) (dual of [4782998, 4782858, 23]-code), using
(118, 140, 4448367)-Net over F9 — Digital
Digital (118, 140, 4448367)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9140, 4448367, F9, 22) (dual of [4448367, 4448227, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9140, 4783003, F9, 22) (dual of [4783003, 4782863, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(9134, 4782969, F9, 22) (dual of [4782969, 4782835, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(9140, 4783003, F9, 22) (dual of [4783003, 4782863, 23]-code), using
(118, 140, large)-Net in Base 9 — Upper bound on s
There is no (118, 140, large)-net in base 9, because
- 20 times m-reduction [i] would yield (118, 120, large)-net in base 9, but