Best Known (114−25, 114, s)-Nets in Base 9
(114−25, 114, 4922)-Net over F9 — Constructive and digital
Digital (89, 114, 4922)-net over F9, using
- net defined by OOA [i] based on linear OOA(9114, 4922, F9, 25, 25) (dual of [(4922, 25), 122936, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9114, 59065, F9, 25) (dual of [59065, 58951, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9114, 59067, F9, 25) (dual of [59067, 58953, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(9111, 59049, F9, 25) (dual of [59049, 58938, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(93, 18, F9, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(9114, 59067, F9, 25) (dual of [59067, 58953, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9114, 59065, F9, 25) (dual of [59065, 58951, 26]-code), using
(114−25, 114, 57478)-Net over F9 — Digital
Digital (89, 114, 57478)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9114, 57478, F9, 25) (dual of [57478, 57364, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9114, 59067, F9, 25) (dual of [59067, 58953, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(9111, 59049, F9, 25) (dual of [59049, 58938, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(93, 18, F9, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(9114, 59067, F9, 25) (dual of [59067, 58953, 26]-code), using
(114−25, 114, large)-Net in Base 9 — Upper bound on s
There is no (89, 114, large)-net in base 9, because
- 23 times m-reduction [i] would yield (89, 91, large)-net in base 9, but