Best Known (112, 112+30, s)-Nets in Base 9
(112, 112+30, 3939)-Net over F9 — Constructive and digital
Digital (112, 142, 3939)-net over F9, using
- 91 times duplication [i] based on digital (111, 141, 3939)-net over F9, using
- net defined by OOA [i] based on linear OOA(9141, 3939, F9, 30, 30) (dual of [(3939, 30), 118029, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(9141, 59085, F9, 30) (dual of [59085, 58944, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(9141, 59089, F9, 30) (dual of [59089, 58948, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(910, 40, F9, 6) (dual of [40, 30, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(9141, 59089, F9, 30) (dual of [59089, 58948, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(9141, 59085, F9, 30) (dual of [59085, 58944, 31]-code), using
- net defined by OOA [i] based on linear OOA(9141, 3939, F9, 30, 30) (dual of [(3939, 30), 118029, 31]-NRT-code), using
(112, 112+30, 68647)-Net over F9 — Digital
Digital (112, 142, 68647)-net over F9, using
(112, 112+30, large)-Net in Base 9 — Upper bound on s
There is no (112, 142, large)-net in base 9, because
- 28 times m-reduction [i] would yield (112, 114, large)-net in base 9, but